Unless you have a coapplicant who can cover all of your liabilities comfortably then the ability to repay is not evident. Under the new QM/ATR (qualified mortgage/ability to repay) laws that went into effect under Frank-Dodd on 1/10/14 it could even be considered illegal to give you a mortgage.
If you omit the information and are somehow able to close then you would be committing mortgage fraud.
Either way why risk it? If the loss of your job affects you qualifying then your lender can provide you with a decline and your earnest monies can be refunded.
Plus it's easier and cheaper to get out early on in the transaction,,, consult with your agent and lender if applicable.
If you had another job lined up you might have a work around available depending on the loan program but your timeline is likely an issue.
More than likely you will not get final approval for the loan given the circumstances. I would err on the side of caution and have your agent talk to the other side as soon as possible. There is no gaurantee that you will be employed in the same city so why tie yourself to a house that you will need to rent or sell. Joan Bowyer-Principal Broker-John L. Scott-32 years of helping buyers and sellers
If your termination is a public matter and the bank will find out, they will likely not approve the loan at the last minute. Employment verification calls are not uncommon and sometimes happen more than once in the underwriting process.
I think I'd find out if there were other jobs in the company you might be able to get. I would be looking for other employment opportunities outside the company and I'd be talking to anyone else involved with your decision making for their input and advice, like a spouse.
I had something similar happen to a client of mine before and we just stopped our process until things worked out. Eventually he got a much better job and we got their home sold and they got a much larger home that they love.