The Big Gold Book doesn't cover this fairly common event, but from experience there are a few options, some of which work better than others. Keep in mind that BRP is a toolkit game—there are few things you can do wrong so long as how you choose to do it works well for the group and the needs of the gameplay and story.
The most punitive options, such as losing their action that round or being forced to continue it (to mortal or comical results), are the simplest but the least satisfying. They're very satisfying for the players when it's a villain who suffers, but in practice it's the player group who will be experiencing the effects of this ruling far more often, and the satisfaction of seeing a villain's statement invalidated won't make up for the many more times their own actions will be invalidated.
In practice, too, these most punitive options often don't pass the most important test: do they maintain suspension of disbelief. Being force to lose an action or continue an action that has become self-defeating or dangerous often leads to arguments both because its unwanted, but also because often enough they aren't easily accepted by the group as a believable outcome.
The options (two, used in different circumstances) that I've found work nicely are more permissive, but have the virtue of keeping the action moving without frustrating anyone unduly (including you, when directing an effected villain).
Have the player make a new statement on the spot when their turn comes up, but then delay their order in the turn. A −5 DEX rank that mirrors the penalty for taking multiple actions (p. 190) is pretty reasonable—it provides a bit of delay between statement and action, and it mostly maintains suspension of disbelief. Mechanically it can be thought of as if they're taking two actions, except the first action is a non-action and doesn't use up their normal allotment of actions.
You still have to decide how to handle it when the penalty drops them below DEX rank 1 though: do you just have them go last, or do you treat it (as on page 190) as if the action is lost? Either works, though I prefer the second as being more consistent and as sensibly penalising those characters who are simply too slow in combat to recover gracefully from unexpected changes. And, combined with the second option below, it only gets applied when it makes sense.
Let them immediately choose a new statement and resolve that action on their turn, but only one that's an obvious alternate course of action (like "stop at the edge of the collapsing bridge" instead of running onto it) or closely related to what their original statement was.
An example is in order. The most obvious use for this option is during a melee, where a player's statement was something like "I will attack the big orc with the bone necklace" and then that opponent is downed before their turn. In such a case it seems eminently reasonable to me that they could simply attack one of the other engaged opponents instead, with no delay at all.
I like this option for when it would seem odd for there to be any confusion or delay in their course of action due to changed circumstances, but technically they still can't fulfil their exact statement. Statements of movement that turn out to be impossible later in the round (like the bridge example, or a closed door) don't seem to be befuddling enough to cause any delay, just a slight change of destination — stopping before the missing bridge; moving to and trying to open the door instead of simply walking through it; going left around the column instead of right because something has moved in the way — such things don't justify delaying or losing the action at all. Being able to just slightly redirect the course of your feet or of your sword in-the-moment is something a competent person is capable of, and not allowing it when it's obviously the natural response to changing circumstances breaks suspension of disbelief for me.
So those are what I find most reasonable: allow a slightly altered statement when reasonable, and otherwise allow a completely changed statement with a bit of a delay.
But again, it's a toolbox, and I find reasonableness to be the best guide of what tool to use at any given time. During play, if a way of handling it seems obviously superior for the circumstances, follow your gut and explain how it will be handled this time, and why, and the group should be fine with it. If something so stupifyingly stupendous happens to invalidate an action, maybe that one rare instance it does make sense to have them completely lose their invalidated action. Trust your ability to model the narrative with the mechanical tools the game provides and suggests, and develop the skill to improvise a ruling on the spot, and games will flow nicely.