I dont know much about the ins and outs of these kinds of contracts but there is no question of Woodward having missold anything, there are no guarantees in sport and Adidas will know that perfectly well. I would assume, but it is only an educated guess, that a sponsor can terminate a contract on the basis of the kind of criminal or corruption-based situation like the one in athletics. But being a bit shit isnt the same thing at all, that would surely not provide the grounds for a sponsor to terminate a contract. Especially as we already know about a clause that says their payments are reduced (not terminated) if we fail to get into the CL two seasons in a row (or something like that, I forget the precise details).
So while I can imagine sponsors being hugely disappointed, pissed off even, I dont think it would be a question of Woodward having to bribe them to stay. Yes he'll want to keep them sweet, especially some of the shorter term contracts (unlike the Adidas one) that may not be renewed if we dont sort things out soon. But I cant imagine things are as precarious on that front as you are making out.