In many situations a persons private residence wasn't always a separate residence/location the way it is today. Farming would be one obvious example of people being housed on location in a variety of housing options like bunk houses or small cottages. Army barrack housing would be another classic example. Or English manor houses with their attic dormitories, separating Male/female staff. The result of these styles of communal living is that you don't have to go far to inform whomever it may concern that you are ill (Or someone would come looking for you at some point). Self-employment or cottage trades are also straight forward, if you don't work you don't make a living.

If your living situation was such that you weren't that immediately local you might also send a message with someone like a messenger or older child as a runner.

The question of what happens when returning to work from an unexplained absence is not particularly historical in context. Much like today, it would depend on how sick an employee actually was/could prove and how charitable the boss is feeling.

In major cities there were once multiple mail deliveries each day.

Residential customers would have morning and afternoon, while business district customers might have 6 or 7 deliveries. If one were sick, one could mail the boss and they would receive the message that day.

NYC had pneumatic tubes for transmitting mail between offices. Mail could move from upper manhattan to Wall Street in ~20 minutes. An hour or so door-to-door for mail speed.