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The heel becomes cracked through and the cheeks of the pegbox no longer have anything to keep them from pulling forward under string tension. 

Like this:

Since the cheeks project past the sides of the neck, there's ordinarily nothing much to keep those cheeks from pulling forward under string tension. When the wood breaks, which happens easily, you have trouble. 

Here's a simple scroll repair that involves installing a different kind of nut (shown below, in red). 

In the case of a bass, you have to begin by taking the tuners off, to get the plate (the whitish outline in the sketch below) out of the way. Afterwards, though, the tuner plates will help cover the scene of the crime. 

First, you glue everything back as it was before the break. Then you reinforce the repair. 

The idea is that the new nut acts as a transverse bar which bears the forward pressure of the cheeks of the pegbox, which was formerly held back by nothing but the lateral strength of the grain of a little bit of the wood beneath the nut, and distributes that load differently. 

The nut in the top sketch is a bit exaggerated, but setting it down some below the neck/board seam at the end of the fingerboard, as in the sketch, is probably a good idea. This way the scroll pressure is bearing on both maple and ebony.

Basically the back of the nut should elide with the plane of the inside of the scroll box, as shown in the sketch in x-ray vision, in the top sketch. 

The nut should be a pretty tight fit, so there's no slack to begin with. Even a very tight glue joint will flex under that much tension, and the less flex that's possible, the stronger and more durable this repair will be. 

I've not had a single failure with this technique. It's way better than pins, bolts, dowels (particularly), and it's fairly easy to do, too. It's also easy to make it cosmetically acceptable, for all that's really different visually is the ends as they're mortised down into the scroll a bit, and most of that is covered up by the plates of the machines. 

Q:  Are you saying that there is no need to pin the chin of the scroll? 

Right. I have only done that a couple of times, and in retrospect, I think it's not only unnecessary, but may pose a potential problem. I think pins create as much weakness as they theoretically supply. I have seen too many pins fail. Wooden ones compress, as does the wood around them. A vacuum-fit metal pin might work. 

Q:  Do you cut a slot in the cheeks of the scroll so the new nut runs totally across from side to side.  From outside edge to outside edge. 

Absolutely, all the way, the mass of it is its strength. One could conceivably let it into the same area without breaking all the way through the ends, to conceal it. This would require some slop in the ends of the mortise to accommodate breathing of the scroll. Much like the slop left for the saddle under the tailgut. 

Q:  Do you use ebony? 

Usually, unless it's some dreadful Kay/Engelhardt thing from a school, in which case I use any substantial dark, hard wood I have. It's mechanically locked there, so even glueability is not an issue. There are a number of mystery Mexican rosewoods that show up in local wood yards and I keep the scraps from other projects for things like this. One is called Cordia, aka bocote, and it's actually really nice for nuts, as it seems to have a bit of  built-in lubrication, works easily, and it's nice and dark too. 

I think the plates of the tuners are very important structurally. For this reason I greatly prefer two-on-a-plate type gears over singles. 

Basses take a beating, and need all the help they can get.

The above repair is what I would consider fairly elegant and one that I would do to almost any instrument, since it's reasonably aesthetic and surefire. 

Sometimes the aesthetics of the side of the pegbox need to be preserved, as below. Notice the nice carved border. 

In the shadows below the nut you can see the crack. Five strings!

Here's how to possibly do the same repair invisibly:

Remove the nut. Note the red lines indicating the cracked cheeks.

Next, inlay a deep trapezoidal 'key' of very hard wood spanning all the cracks under the nut. The grain should run side to side, so the string force of the scroll is bearing on the slab of the key and that pressure is being transferred to the barrel of the neck itself.

Side view of the same. You're looking at the endgrain of the concealed key, blue-green. This key needn't really go much lower than the crack itself, since it's the area above the crack that does all the work.

(It would approach overkill, but if you wanted maximum strength from this key, you could laminate it from three layers of hard wood with the grain of the layers at angles, so no cracking would be possible.)

Afterwards, put a nut back on over it. The repair will be completely enclosed and invisible. The effect of the repair will be the same as the inlaid nut above. I would use a good 12-hour epoxy, well mixed, for this, because it fills gaps and remains absolutely hard. 

Here's a bit about the two main base-of-neck repairs I encounter, and how I deal with them in less expensive instruments:
 

 

This is a very reliable, if inelegant, repair. The image pretty much says it all. First I remove the fingerboard (I really dislike the look of a plug in the board itself), then glue the neck back together. Then I make the holes for fitting the ends of the bolt. The end holes need to be flat-bottomed, so the cap and nut of the bolt are bearing on solid platforms of maple, and just deep enough to allow everything to fit in there - the head and nut, washers and so. The end holes need to be made first, and in sufficient diameter to receive a thinwall socket that fits the head and/or nut of the bolt. 

Then I drill a hole through that's precisely fitted to the shaft of the bolt, starting at each end from the centers of the larger holes, aiming to connect the two holes in the middle. This is more easily eyeballed with a power drill than you might think. 

Note: the end holes can be situated in such a way as to allow you to angle the through-bolt back and fairly close to the in-curve of the heel too:

I expect wood to compress over time and I expect to possibly have to tighten the bolt (I at least wish that to be an option). Therefore I situate the cap of the bolt at the heel, and a nut with a lock washer under the board itself. This way, the plug or cover in the heel can be removed and the cap of the bolt can be tightened if necessary, which is easier and much less messy than removing the fingerboard. 

Once the connecting 3/8" (or whatever) hole is drilled, the bolt is installed and tightened to the max. Reattach the fingerboard, cap the hole in the button, and so on. 

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OK, here's another more draconian approach to a neck that snapped off with the button sheared off the back and still attached to the neck. Again, there are delicate alternatives to this kind of repair for good instruments, but this gets a laminated school bass solidly playable again, at least cost:

 

After gluing the neck back on, I fashion a plate from a thick piece of brass or stainless. I use stout oval-headed screws, preferably stainless, and countersink the brass plate to receive the heads. Given the lack of right angles, this is necessary. The single screw is carefully sunk into the end of the heel of the neck; the other two screws go into the neck block. Correct pilot holes are obviously necessary. I have on occasion drilled and tapped a machine-screw hole into the maple, to make for maximum fit and to avoid splitting. 

Even when high school kids drop the bass down the stairs and the neck comes loose again, this plate will keep it together until help arrives.

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Finally, here's a variation for when the button of the heel is broken off and still attached to the heel of the neck, and the neck is also cracked:

Here's a sketch of the cauls and clamping method which make it possible to glue a neck back on (or back together) with a single clamp. Notice the angle of the cauls at the red arrows. The green arrows show the way those cauls are inclined to slip under pressure, which augments their tightening and resists slippage. 

There are some really elegant approaches to repairing damaged necks, but they take a lot more time.  This is a repair I have done on a few good cellos that had the ultimate nasty break through the heel higher up. These were ones that I didn't want to insult with a bolt or something. 

It's a maple spline that I make with a router from something like full 1X stock. With the fingerboard off, and the neck off and the heel glued back on, I make a jig to hold the neck and route a round-bottomed channel with a matching router bit for the spline that runs the entire height of the heel. Once the spline is glued in, you trim it top, face and bottom, to the original surfaces of the neck, and reattach the neck to the body. There is nothing visible once it's reassembled except in the overstand under the board, which you can conceal pretty easily (only trolls hang out under there anyway).

Since the spline now constitutes 80% of the volume of the heel, it will never move, or if it does, it will all move in concert. That crack will never budge. I leave a small (1/64) gap at the ends of the spline so the sleeve of original maple can breathe a little without the spline pushing on the button or the underside of the board. 

In the right instruments, this is time well spent, of course. It's solid and invisible. The ones above, with bolts, are only for instruments in schools with little or no repair budget.