Who introduced proof text into the discussion. Support I will allow.
It means both are disallowed.
The text indicates the stripes are punishment given when the LORD judges that servant. For the myriads of servants in the two millennia since their passing I would read that as the very night of their death. How long the beatings continue depends on what was committed to them, and what they did with it. The parable is a master disciplining his servants upon his return. One servant’s behavior is so egregious he is assigned a portion with unbelievers. Other servants are beaten. Another servant is made master over the entire household. All of this is according to their works mitigated by their understanding of the master’s orders.
The master is the Messiah. The little flock, and others, are the servants.