Reception should not print its receipts on the restaurant counter. The bar's drinks should not appear on the grill printer. Once a property has more than two devices, "which printer" stops being a property-wide setting.
Resolution walks four tiers, most specific first: this terminal and this station, then this terminal's catch-all for the role, then a printer bound to the station, then the property default. The first match wins outright — a terminal-specific mapping replaces the default rather than competing with it.
With no mapping configured at all, the outcome is byte-identical to having no routing feature, which is what makes it safe to ship to properties that will never open the screen.
A dead or soft-deleted printer is filtered out explicitly rather than routed to. Sending a slip to a device that no longer exists is worse than falling through to the default: the slip vanishes with no error anywhere.