They would have to, which is why they are stuck with him. If they cut him for skill or cap reasons, he still gets his money.
"There are three separate kinds of guaranteed money
When utilized, the full guarantee of a contract consists of a combination of skill, cap, and injury guarantees, rolled into one deal.
The skill guarantee is unique in the sense that it's meant to protect a player from losing his wages if he were released. In this case, a player would receive guaranteed money if losing a roster spot was due to the declining of his skills in relation to his position. For example, a veteran place kicker who's gradually missing more and more kick attempts loses his job to a more accurate kicker, but will still be paid his full salary, after he's cut from the team.
The cap guarantee will ensure a player is paid in the event he is released for salary cap reasons. The most common situation here is when a team releases players to free up cap space, to be used in signing new players. This, like the skill guarantee, would promise a player's full salary should he be released."
Why would he, after signing the contract, negotiate away any money--as they are cutting him??