There's no official answer…
Ask the GM what happens if a creature sticks its arm in a bag of holding and then pokes the bag with a sword until the bag rips. That's the best—and, really, only—way to find out what'll happen in a specific campaign.
…However, the task described is impossible in this GM's campaigns
In this GM's campaigns a creature or object is either on one plane or on another plane and not simultaneously on two planes. Because a bag of holding is less like an actual bag and more like a portable portal to another plane, a creature can take either a move action or a full-round action to retrieve an item from the bag, or a creature can take a move action to stow an item in the bag. A creature can't, in this GM's campaigns, opt to stick only its arm in the bag and leave his arm there while he goes about his day anymore than a creature could store just the bottom quarter of a tall tree within a bag and leave the top of the tree hanging out of the bag. Instead, the either the creature puts something all the way in or the thing doesn't go in at all, and, likewise, either the creature enters the bag completely or the creature doesn't enter it at all.
While this GM admits that this is a kind of no fun ruling that eliminates a lot of bag of holding shenanigans, this ruling also means the GM doesn't have to figure out what happens if, for example, the PCs go to a fast time trait plane and have their golem walk around with the PCs in a bag of holding while only the PCs' heads are sticking out so that their heads age and not the rest of their bodies (so that they can benefit from the increased mental ability scores that come from aging but not suffer the lowered physical ability scores due to aging… obviously). Not having to worry about stuff like that makes this GM's life easier.