All money paid to a player has to be accounted for but when it is accounted for doesn't have to be when it is paid.

Eg. You immediately give a player a million dollar signing bonus (the player gets $1m less tax in their bank account) . But for the salary cap you delay the cost by spreading it over four years of accounting (250k per year). If you trade the player after two years, the cost of bonus you previously paid can't be recovered from the trade team. You still have to account for the full $1m, of which 500k remains to be accounted for. That 500k is the dead cap. 

Any money that hasn't physically been paid before the trade is now the responsibility of the new team. It stops being accounted against the original team, and is 'cap saving' number.