We tend to refer to it that way, because it makes his cap hits in subsequent years higher. Typically, a restructure just turns his base salary into another "signing bonus". So, for next year, you would take his 12.25 million and spread that out over the remainder of his contract, which is four years in total. He still gets that 12.25 mill this year. It significantly lowers his cap hit this year, but makes the cap hit higher each of the next three years, making it harder to cut him because of the increased dead money that would be involved. So, in that sense, it could make the team hold onto him longer than they would have otherwise, effectively "guaranteeing" him more money.
If Dallas fully restructures Demarcus Ware's 2014 base salary of 12.25M, it would mean dropping the salary down to the minimum, $0.855K in Ware's case, and converting the remaining $11.395M into a signing bonus. It would be spread over the remaining four years ($2.84875M per yr) or the team can add a fifth season to enable maximum proration ($2.279M per yr).
Ware gets that bonus money paid up front, but it counts in equal amounts against the cap for the remainder of the contract.
This restructure would push either $8.54625M (4yrs) or $9.116M (5yrs) in new bonus prorations into 2015 and beyond.
If Ware get released, this is what becomes "dead money." (along with any other remaining prorated bonus money from past restructures still on the books).
The team doesn't actually owe the money to the player, it's already been paid, but it still counts against the salary cap.
When a player is released or traded, all remaining pro-rated bonus money in future years will escalate into that year's cap unless the June designation is used or it takes place after June 1st.
Dallas can do the restructure, create cap room, and revisit Ware's contract again next year or they can have "the talk" and try to work out a compromise that's fair to both parties.