Ned is a Hexblade Warlock. He found a magical net+1 and made it his pact weapon via his Pact of the Blade feature:
You can transform one magic weapon into your pact weapon by performing a special ritual while you hold the weapon.
Note that pact weapons can be ranged, and ranged pact weapons can be summoned or dismissed as normal.
You can also use Pact of the Blade to bond with a magic weapon, turning it into your pact weapon. This magic weapon doesn’t have to be a melee weapon, so you could use the feature on a +1 longbow, for instance. Once the bond is formed, the magic weapon appears whenever you call your pact weapon to you, and you can’t change the magic weapon’s form when it appears.
However, nets can be destroyed:
Dealing 5 slashing damage to the net (AC 10) also frees the creature without harming it, ending the effect and destroying the net.
Now Ned has become rather fond of his net, and would prefer to be able to continue using it after it has been so ruthlessly slashed by the angry goblins of the mountain caves. He knows that it's possible to mend broken items, and is willing to spend time and money (or find a wizard to cast mending) to fix his net if possible. But if destroying Ned's beloved net means that it's no longer his pact weapon, all that effort is for nothing - besides, repairing a destroyed magical net may or may not preserve the net's magic.
I couldn't find any official rulings about what happens to destroyed pact weapons. This question is about pact weapons in general: a net is just a convenient example that can be easily destroyed.
Is a destroyed pact weapon still a pact weapon?