In Jain Dharma, the principle is Ahimsa: one should avoid harming any living being, even a small insect like a fly.

So:

• A śrāvak/śrāvikā should try to protect the fly if it can be done without causing greater violence.
• A muni follows even stricter Ahimsa, so he should also avoid allowing harm if protection can be done without breaking vows or causing injury.

But Jainism also teaches careful judgment:

• If saving the fly will cause more harm to other beings,
• or if it requires violent action,
• then one should not do it in a way that creates greater violence.

So the Jain answer is:

Yes, if the fly can be saved by non-violent means, one should save it; otherwise one should act with maximum care and minimum harm.

In short:

• Save if possible
• Never increase violence
• Follow Ahimsa with discretion