need to check your county's laws to see what the requirements are. Not an attorney but my sense is that yes than can evict for being late but that if they accept the funds they have to honor the period you paid for After that is up then they have to follow the procedure for giving you notice that they wish for you to leave. depending on your lease would determine the amount of time you have. You can fight it I suppose and see what happens. It doesn't matter the reason you are late. Landlords are not obligated to be empathetic to your situation, although some are. A judge on the other hand may allow you stay for a certain period provided you put money on deposit with them.... goodluck..