Napkins are rarely retired because of stains. They are retired because the corner went.
What a serged edge is
Serging wraps thread around the raw edge of the fabric to stop it unravelling. It is fast, it is cheap and it is genuinely fine on garments that get a domestic wash.
In an industrial laundry it is not fine. The cloth is agitated hard, spun, and tumbled against hundreds of other items, and all of that load finds the corner. Once a few threads go, the corner unravels and the napkin cannot be reissued.
What a mitred, double-turned hem is
The edge is folded over twice, so the raw edge is enclosed inside the fold and nothing is exposed to the wash at all. At each corner the excess is cut away at an angle and the two folds meet in a clean diagonal — a mitre — instead of building up into a hard lump.
That lump matters more than it sounds. A bulky corner is what catches, and it is also what stops a napkin lying flat in a stack.
The stitch
A lockstitch, not a chainstitch. A chainstitch can run — pull one end and a whole seam can unzip — which is exactly the failure you do not want on an item handled by a hundred people a day.
None of this is exotic. It is the standard construction for hospitality napkins and it is the first thing removed when a price has to be hit.
What to ask a supplier
Three questions: is the hem double-turned or serged, are the corners mitred, and is the stitch a lockstitch. If the answers are vague, the answers are serged, no and no.
It is the cheapest specification on the quote and it is the one that decides how many seasons the stock lasts.