It depends on what you mean by "collapse".

If there were no miners, then transactions could not be "confirmed", and the blockchain would stop growing.

All your existing bitcoins would be secure, and transactions could still be created and relayed between peers, but double-spend attacks would become easier, so it would be more difficult to trust a transaction that you receive.

Would this cause everyone to loose faith in bitcoin and abandon it?  Probably. And that would result in a collapse.

HOWEVER . . .

As long as a bitcoin has any value at all, why would everyone stop mining?  Someone somewhere would see the opportunity to earn some additional value by starting up a miner.  They would get all the block subsidies and all the transaction fees.  Then someone else would want some of that money as well, wo they also would start up a miner.  Before long there are plenty of miners and the blockchain and confirmation process is right back where it was.

As long as bitcoin has value, people will continue to run miners.  As long as people continue to run miners, bitcoin should have some value.  It is intentionally designed as a positive feedback loop.