Got hired for a new company, put my 2 weeks on my job to prepare myself and now the new company is lengthening the start date.

I got hire for a position that I wanted, Everything was well prepared. I wanted to make sure that the contract was signed before actually leaving my old job. We negotiated June 4th and Last week I receive an email saying that one of the branches has been closed and they needed to readjust everybody to a new branch (where am I supposed to go) to not fire anybody. I try to contact the guy, no success in the same day, but the following day he replied to me assuring that everything was going to be fine, the account was steady and reliable and he needed to change to June 11th. I felt better more secure, but today i received another message delaying the date again. My thoughts is:

Since i signed a contract, they're trying to make me quit to not pay any of unemployed tax or anything related (correct me if i'm wrong)

What should I do? Is there any place to go now? The pandemic made everything harder.

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