The environment within a cell is actually rather reducing, this is evidenced by the free cysteine found in some proteins. Many proteins require a free cysteine to operate properly, and once they’re outside the cell, they can easily become oxidized. Enzymologists have had to deal with this for some time since we started taking oxidizable stuff out of cells. Just over 40 years ago, Cleland realized that dithiothreitol would probably work pretty well for this.
Using thiols for a reducing agent is a common strategy; the idea is you dissolve much more reducing agent than protein (often in 1,000-fold excess or more), and the thiol will sacrifice itself to reduce any R-S-S-R to R-SH, getting oxidized along the way. DTT works especially well because it forms a six-membered ring upon oxidation: