Disclaimer: I have never had to deal with having a team in my leagues that had a vacant spot on the roster.
After skimming through the USBC rule book it appears that the team could go through the season like this. I have seen our youth league wind up with one or two team with a vacant bowler on the roster but I have almost no idea how the details of that work out. Since the team in your league is not making a good faith effort to fill the spot the team would be required to pay for the spot. I would assume your center will be willing to only charge lineage for the actual number of bowlers so the vacant fee might only be the prize fund portion of the weekly fee. It could be the whole thing.
USBC suggests that the vacant score for adult leagues be 120. But the the league may set its own number. They also say that the handicap for a vacant score be calculated the same as for a regular bowler. It does say that a league may adopt a rule using a lower handicap, say 0% to discourage teams from using a vacancy score any longer than necessary.
Personally, I think if the members of a team are willing to put in the extra money each week it’s fair. While the vacant spot is never going to have a bad game, it’s never going to have a great one either.
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