Can severence be rescinded after signing to receive it over an unreasonable job offer?

My company is consolidating branches, and offices are closing. As a result, I was approached by HR with an internal job offer. This offer was considered to be unreasonable as it would reduce my position from full to part time. Because of this, the offer also stated that I could choose to become a displaced employee and would receive severence benefits. I choose to not accept the offer and take the severence. I signed where applicable and returned the form to HR within the 24 hour window I was given to make that decision. Now, a month and a half later, the company is saying that severence is off the table because they made a mistake with the model, and will need more fulltime employees. I have already made arrangements to move, and other decisions based on the agreement I signed. Is it legal for the company to come back at this point and void an agreement that has already been signed and agreed upon?