???
The post office has no idea about what has been delivered and what has not been delivered, unless its Cetified Mail. If it was Certified Mail, then you have legal recourse.
The courts and IRS only accept Certified Mail as being timely mailed.
(I have seen this sort of thing happen on the fast growth end of an oil boom, when there was just not enough housing and people were staying in tents with winter coming on. Rents skyrocketed and no lease was worth the paper it was printed on.)
Then make sure you get all the 'i's dotted, and 't's crossed on time--while you look for another place.