If the club was broken in anger - for example, as a result of being slammed into a tree or thrown down the fairway - it cannot be replaced.
If, however, the damage occurs "in the normal course of play" - e.g., the clubhead snaps off a driver during the swing, or an iron is bent when trying to play from under a tree branch - there are options for replacement (see Rule 4-3).
The first option: Keep playing with the damaged club (not much of an option, eh?).
The second option: If it can be done without unduly delaying play, you can repair the club yourself, or have it repaired by someone else.
The third option: If the club is unfit for play, you can replace it in your bag with any other club, as long as play is not unduly delayed. The replacement may not be borrowed from any other player. But you can get it anywhere else - from the trunk of your car, from your locker back in the clubhouse, from the pro shop, from your Uncle Harry who always carries an extra club for you just in case.
In Decisions 4-3/1 and 4-3/7, the USGA cites other specific examples for when replacement is and is not an option.
Replacement is OK if the damage occurs: upon normal removal or replacement from the golf bag; while using a club to search for or retrieve a ball; by accidentally dropping a club; or by leaning on the club or using it as a cane while walking.
Those situations are among the examples of a club being damaged "in the normal course of play." Examples of damage that occurs not in "the normal of course of play" include damage as the result of angry actions (slamming the club into anything, including the golf bag; throwing it, drop-kicking it) or intentionally striking something with the club other than during a stroke or practice swing.
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