Contracts in the NFL only loosely fit the definition of what a "contract" is intended to be. Basically an NFL contract is a salary/payment structure and anything beyond the current year is essentially meaningless.
A really exceptional player has the ability to essentially void their contract every 2-3 years, regardless of the terms of the contract - the team also has the ability to release a player they feel isn't meeting their standards while only being on the hook for a portion of what was agreed upon by both parties.
It's a two-way street, in a sense. Because teams can release a player with little regard to what was agreed upon in the contract, players are more inclined to fight for more money when they have played to a level that exceeds the "going rate" for that position. As unsavory as a holding-out player can seem, it acts as a form of "checks and balances" for the player/team dynamic.
Where it gets a little muddled in the public perception is that for a team to use their leverage by releasing an "underperforming" player it can easily be explained away as "we are doing what it best for the team" - which makes fans happy because, that money will go to someone potentially better than the released player and equal more wins.
In order for a player to use their leverage, they have to withhold their services and force the team to give them more resources than were originally allotted for that player - which of course means that there is less of the pie to go towards resigning other players or brining in new players.
In the eyes of fans - that's a bad thing. So the player seeking more money is usually vilified.
The biggest issue is that it's all extremely unbalanced. Only the upper-tier players hold the negotiating leverage. Guys like Murray are in the "good, but very replaceable" area, so they have little leverage in negotiating for more money.
Often, as we saw with Murray, teams will balance the books on the backs of those players. They will essentially come with the ultimatum - "you are overpaid for your production level. Take a pay cut or we will release you."
The player can agree to that, if they agree with the assessment - then they play out the new terms and walk when the contract is done. Or they can say, "I don't agree with the assessment - or I do but would rather play somewhere else for less money than stay where I'm undervalued." Which is what Murray chose - and he will likely go to the Ravens where he will be on a good team.