The fact that they are trying to prevent you from going to a tribunal does not necessarily mean that there is likely a case there, it is just a clean break for both parties and peace of mind for the employer that this is the end of any potential issues with you. Of course it could be that there is a potential claim but based on the very limited information I have it is difficult to tell you if that is the case. What would happen however is that if you are willing to consider the settlement agreement, to make it valid you would have to go and see a solicitor in person, who would look at the terms of the agreement and consider the overall situation and advise if it is reasonable to accept it. If you think that there is a claim and have been told of this then you are not bound to accept the offer and can continue negotiating for more, using these arguments as leverage. So there is still an opportunity to seek formal legal advice before you are able to sign it and make it binding.
As to TUPE, that is not something that the employer can make a decision on and whether they keep you or you have to move to the new employer – this happens automatically if the criteria for TUPE are met, such as the transfer of a business or a service.
It sounds like you are most likely to consider a settlement so indicate your preference for this then go and see a solicitor, which the employer should pay for and consider if this is indeed a good deal for you to leave under, then make the final decision.
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