Another version is: ‘Don’t overrun the constable.’ This has nothing to do with
not running faster than a policeman, or shooting past him when he is on point
duty. It means: ‘Don’t get into debt.’ In olden days police constables acted
as debt-collectors. For example, if a tradesman allowed his customers one
month’s credit, and a customer failed to pay at the end of that period, the
tradesman might call in the constable, and the debtor might well be sent to
prison. So, ‘to outrun the constable’ was to go beyond the point when you were
safe from the arm of the law.