Who likes to defend? It is very annoying to have a bad position. However, to be in a bad position without any hope for a counterplay is almost a physical suffering for a chess player. Any stronger chess player would prefer unhealthy, but complicated position to slightly worse endgame without counterplay.
David Navara tried to get off the hook in the 3rd round of Tata Steel Chess Tournament. He was a pawn down with Radjabov and he would need to demonstrate a very strong defense under normal circumstances. See the article and analysis by GM Jan Markos.