Rechargeable batteries should have a relieve valve, to prevent it from actually blowing up.
Overheating will generate gasses, which will come out one way or the other.
A relieve valve will offer a way out, but of course the battery will be damaged after that.
If there isn't a way out available, an alternative will be forcefully created.
A standard battery doesn't have a valve (too expensive to create).
The release of the gasses doesn't need to be a speedy process.
With a lesser current (but still too high) it might take a while before the battery blows.
Any component has some resistance.
That of the battery will be the highest, compared to wires, breadboards and switches.
So it isn't impossible for other parts of the circuit to come out relatively undamaged compared to that battery, they should be inspected though.
I'm not sure whether the heating up of that battery will create a higher or a lower resistance.
If it goes down, an avalanche effect will occur and the destruction will be speedy.
If it goes up, the battery will live it's (by then miserable) life a bit longer.
The reason for rechargeable batteries to have this valve, is the charging process.
A too high charging current will also create gasses.
Some rapid charge methods also incorporate discharging too.
It will rapid-charge for a while, in such way that small gas bubbles are formed.
After a set time, a very short but high discharge pulse will be created, which is supposed to revert the gasses.
I remember some Elektor project (about 20 years ago) where this was explained, and played around a bit with this ICS1700N based project.
That process is explained in datasheets for that chip that can be found online.