What does False Swipe do?

Answer 1

It leaves the foe with at least at 1hp.

So, this move is very useful in catching the Pokemon you want especially on legendaries.

If trying to catch legendaries bring a Pokemon that knows this move with a significantly higher level to that legendary. Otherwise, the move will probably not work to its full potential and not leave it with 1hp.

Pokemon That Can Learn False Swipe

By leveling up:

• Farfetch'd at Lv.46
• Cubone at Lv.33
• Marowak at Lv.39
• Scyther at Lv.16
• Scizor at Lv.16
• Grovyle at Lv.53
• Sceptile at Lv.59
• Nincada at Lv.25
• Zangoose at Lv.55

By breeding:

• Spearow
• Paras
• Pinsir
• Heracross
• Seedot
• Shroomish
• Mawile

Credit to Uzushio.

What_pokemon_learn_false_swip_in_pokemon_emerald

Answer 2

False Swipe is a Normal-Type TM with 40 Power and 100 Accuracy that always leaves 1 HP. Pokemon with claws or blades can learn False Swipe.