"Crashing" is not a concept in Turing machines. More practically, if you does_halt algorithm "crashes" on certain inputs, then it fails to give an answer to those inputs, and so is not a solution to the halting problem.
There is a real insight in your comment though. There is a weaker version of the halting problem, where the goal is to write a does_halt function that returns yes/no/maybe. That problem is trivially solvable. There are also non-trivial solutions to it that are actually useful.
There is a real insight in your comment though. There is a weaker version of the halting problem, where the goal is to write a does_halt function that returns yes/no/maybe. That problem is trivially solvable. There are also non-trivial solutions to it that are actually useful.