In medieval towns and cities, citizens could be called on to form a night watch under the enforcement of a beadle or constable.
If a call went out to chase down a criminal, every resident of the town had to help or risk getting fined.
But if the fugitive being chased got to a church first, he could claim sanctuary for 40 days. Someone would have to stand watch outside the church day and night to make sure he didn't escape. Towns could be fined for criminals who got away.
Criminals had good incentive to escape though, as punishments could be very harsh. A thief caught in possession of stolen goods was hanged.