Are there any types of tournaments that allow for absences?

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I'm trying to organize an online tournament with about 50 people that will span across 1 or 2 months, and inevitably some people won't be able to play their match every week. Is there a tournament style that allows for this?

I tried doing this before in a swiss-style tournament. The rule was that people who missed a week would have to play an extra match at the very end of the tournament. This didn't work out very well, because there were good players that missed early weeks and then faced easy opponents for the next few rounds. Eventually these good players caught up with the other good players, but then they had an advantage because they still had a make-up match at the end of the tournament that boosted them above the other top racers.

One idea I had to quick-fix this problem was to make the make-up match happen the week immediately after an absence, but I'm wondering if this problem already has a known solution that's mathematically sound.