Okay, maybe partly my fault for using too broad strokes. The fridge example already suggests Midcentury prosperity and civilized employment contracts.
If we're talking deep 1800s, this becomes more complex. As a factory worker, you may not have time and money to buy or own much of anything substantial. But you do have to buy clothes and such. Putting aside extreme examples like isolated company towns, you probably aren't on any long term contract. Why would they give you that, you live in a big city with dozens of factories and tens of thousands of people desperate for work. I'd say this is midway between Uber and how we imagine industrial employment today. If you don't come, they just don't pay you, and if they get mildly annoyed, they can fire you for any reason any time. From what I gather, you would negotiate with the floormaster some very much unpaid time to do a very specific thing, being very careful not to appear "lazy" or disobedient. People did become sick and sometimes returned to work afterwards.
This is based on from I remember from reading contemporary fiction and historiography on the period. But if you think an unmarried worker bought their clothing by some other means, please enlighten us.