I agree, do not open limp a small pocket pair in the bubble of a STT. When playing in bubble mode you want to aqcuire chips without putting your stack at risk in a showdown. In simple terms this means you want to steal blinds from the others in a more efficient manner than your opposition. What you want to avoid doing is taking coinflips and putting your place in the money in jeopardy. You should be the one putting the others all in, not the other way around.

However, the big stack
after me had been playing very aggressively, pushing all-in frequently to
steal the blinds and get people off the hand PF.

This is perfect strategy for this point in a STT, you should be pushbotting all your semi decent holdings, and folding all your average holdings to other people's pushbotting.

By open limping you are inviting someone to steal your money because you simply cannot call in this situation. When someone pushes you all in and you have pocket 4's you are at best a coinflip (he has 2 overcards) and at worst a 4-1 underdog (he has a higher pocket pair).

Worse still, by open limping with this hand you allow the BB to play perfect poker against you. He will raise and call your bets on flops when he outdraws you and he can check and fold on flops that you lead. This means that you have breached the fundament theorem of poker (that you make a mistake when you allow people to play as if your cards were face up).

Also, take the situation where you limp 44, all fold to BB who checks.
Flop comes down QT8, and he makes a pot sized bet. What do you do in this situation? you could very well be ahead but there is absolutely no way of knowing so you have to fold.

You obviously can't play your 4's for set value here because the stacks are so short compared to the blinds, Your M is under 6 so you can't be limping with pocket pairs ans suited connectors hoping to flop something big.

In short, what you should have done is pushed all in preflop, (or folded preflop - I would guess the EV is about nuetral) there is a very strong chance that the big stack will fold and your M will increase by 1.

As played fold to the push.

Thanks for the replies guys.

I was thinking of pushing, but then decided not to. Afterwards, I realised
my mistake.

I feel like i am slowly getting the hang of bubble play, but there is
still some way to go. These topics have really been helping.

Keep up the good work!