It depends on the extent and obviousness of the debris. If it was sufficiently obvious that apartment management (e.g. maintenance staff or property management) should have noticed/seen it and removed it but failed to do so, that would very possibly be negligence and support a lawsuit. But if the debris was not obvious to a casual viewer (since they are not required to go out and carefully search the parking lot for debris), then they did nothing wrong in not removing it and are not liable. There must be fault for there to be liability; the fact that this occured in their parking lot does not, without more, make them liable.Even if they are liable. all you could sue for would be the cost of the tire--the actual loss you suffered. It is not clear if it would be economically worthwhile to sue over that.