Couple things Is it a row house are there buildings on the side or is it a detached home. How tall is the building. Have you seen the basement in question. Do you have access to it at this moment. Have you spoken to the landlord, have you spoken to your room-mate about the situation. Has any load bearing walls shifted or cracked. Can you locate any I-Beams. If you can locate I-Beams do you see damage around them, are they shifted, are there signs of shifting near them. Without having all this information or looking at this building I could say they might've dug out the basement to turn it into an apartment and the foundations shifted. As long as the I-beams in the basement aren't warped or showing signs of warping that means most of the load bearing walls are fine. If you know how to spot a load bearing wall and you see it tilted get the fuck out. The kind of work he's doing requires a DOB permit and an architect, civil engineer and a license and certified contractor. -If- he's digging the basement out. Without knowing what kind of work is being done in the basement this is all a crap shoot. To be safe, get the fuck out. If you don't have a place to go in NYC go to a hotel. With-hold rent, fuck the letters for now. Send those from the hotel/motel/friends couch. Grab as much of your shit as you can and get out. Now for the NOT scary take on this. When you're knocking down walls in a basement in a brick house, the drywall sometimes holds bricks in place. Bricks fall out, crumble, the wall sags a little, you reinforce it with temporary wooden blocks and prop it up. You lose an absolute ton of bricks when you're tearing a basement apart, if he's not actively repairing the wall and just propping it up with wooden blocks his contractors an asshole and that's the reason your outside walls are cracking. Is the house in danger of falling. Technically yes. If the bricks -above- the basement brick wall start domino effecting and crashing down into the basement then yes you're in trouble if he's doing a piss poor job of repairing the walls as he's going along. Honestly I'd rather ask you all this stuff over the phone and give you my advice but I dunno, Reddits weird.