Henry,
In answer to your question, at least on a compound crossbow, several things could happen.
1. Nothing, the cables can hold the bow strung.
2. This can cause the cables to break also
3. If both go, you can bet you need new axles.
4. You can break your limbs an/or all of the above.
It really depends on when and how the string breaks and what bow it is.
Why,are you thinking about trying it?
Randy