If one player reraised and the next player behind does not complete the bet can the next player reraise?
TL:DR; If a player went all in for less than bet. Yes player may re raise. If a player went all in for less than a minimum raise then some players might not be allowed to re raise depending on subsequent action.
The above is correct but as the question has been clarified that the question is about a player being all in for less than the bet then Its worth giving a more detailed answer.
I'm using Robert's Rules from here as reference
Let say blinds are 400-800 in an example 6 handed game. I'm assuming you mean No Limit (as not stated in question)
(I'm assuming understanding of seat abbreviations but if that needs clarifying I will)
The action might go - SB - 400 BB - 800 UTC - fold HJ - raise to 2000 CO - re-raise to 7000 Button - All in for there remaining 5000.
So now the Small Blind fits the example of next player in your question. The small blind can make a re raise again. The minimum being to 12000 as
Any wager must be at least the size of the previous bet or raise in that round, unless a player is going all-in.
If another player does raise of go all in then The button can only win whats in the main pot. In this case that will his 5000. 5000 from the Cut off. If other player call then 5000 from that goes to main pot and blinds (if folded) as well.
the left over 2000 from Cut off is either returned if his raise has no callers/re raisers) or goes towards a side pot.
I think as you've asked the question you may be getting confused about rules for whats I've always known as an 'under raise', when a player goes all in for less than a legal raise. Although the rules link does not use a specific term.
All raises must be equal to or greater than the size of the previous bet or raise on that betting round, except for an all-in wager. A player who has already checked or called may not subsequently raise an all-in bet that is less than the full size of the last bet or raise.
So let change the above example slightly
SB - 400 BB - 800 UTC - fold HJ - raise to 2000 CO - re-raise to 7000 Button - All in for there remaining 11000. (less than the legal 12000 min raise)
If all players before the cut off call or fold then CO only has the option to call the 11000. This is a rare situation where a player is prohibited from raising. However if any player prior to CO raises then the the CO is allowed to re raise that again.
When betting starts anyone can raise.
Even if it is called to the big blind they can raise pre flop on the initial betting round.
If someone cannot cover a bet or raise a side pot is created.
Say the bb raises on the initial betting round. If no one re-raises the bb cannot 3 bet when it gets back to them.
Say UTG 3 bets and UTG +1 is short and has to create a side pot. It is still considered a raised pot and anyone can 4 bet. Except the original raiser unless he got raised.