the mortgage company could take 3 - 4 months of non payment by you to start the court process.
Then potential another 3 - 4 months to conculde the process which should give you ample time to look and find a place to live.
the best suggestion is for you to try and control the process, then you can be settled in your new place all possessions out of the old house.
that means now start looking and speaking to housing authority. Going BR is all about planning (and controlling the process) I took expert guidance who held my hand throgh the whole process