Hello, to give my 2 cents too
The only place they cannot get a hand is between the small blind and the button.
How about this Nick,
The only place a player(s) from a broken table cannot receive hand is if their new seat assignment is between the small blind and the button. Sound better?
Question : who, what, where, when, how this occurs ?
who ? the new arriving player (that is moved),
what? checking each position,
where? on the new table (prepare for the next deal),
when? whenever arriving at a new table, after the end of the running deal,
how? places and position are checked before the next deal.
So il would present this phrasing :
Players going from a broken table to fill in seats assume the rights and responsibilities of the position. They can get the big blind, the small blind, or the button.
On arrival to the new table, places and position are checked before the next deal. After the end of the running deal on the new table, checking applies for all new arriving players (those are moved), players can take their seat.
The only place a player(s) from a broken table cannot receive hand is if their new seat assignment is between the small blind and the button at this checkpoint. If happens, the player can seat, but play only at the next deal.
it is quite clear ?