The only way out for both countries is for Taiwan to offer cash for the island and for China to accept. That way China doesn't lose any face and Taiwan gets what it wants.
Although the Chinese do seem to have a money-oriented culture, offering to pay for the island doesn't seem to be a feasible option.
That's the most absurd idea I've ever heard.
The PRC would lose face if it had to buy what they consider their own territory. They'd rather blow it off the map then do such a thing.
And Taiwan wants to not be under communist rule. Selling themselves into slavery isn't exactly what they have in mind.
I think Taiwan should tell the PRC if they want Taiwan to return to China, they should allow the three political parties in Taiwan to compete on the mainland as the Communist Party and China should change her name from the People's Republic of China to Republic of China (like the one found by Sun Yat-sen in 1911 which was mult party system). Furthermore the flag should be changed from the red field with yellow stars (Communist) to the one in 1911 of the Republic of China. Otherwise no deal.