Patrolling pillagers that whose crossbow broke (or were spawned with another item) will never lower their arms, not even when the player is out of range.

To reproduce for pillagers (identical to vindicators).

1. /summon pillager ~ ~ ~ {Patrolling:1b}
2.  Approach: pillager will rise their arms 
3.  Leave the area: pillager will not lower their arm despite the player being out of range

 The issue sometimes happens to vindicators as well, regardless if they carry a weapon or not.