Should date inputs allow selecting a date in the past?

Our company provides a digital signage system which will allow users to associate a 'lifetime' with pieces the content they create to display on digital signs.

When scheduling is switched on for a slide, we reveal two inputs: "Start date" and "End date". These are date time inputs which can be completed by entering text (numbers), or by clicking the associated calendar picker button.

The scheduling system requires either a start date, an end date, or both. If no start date is provided then the content is already active, if no end date is provided the content will remain active until it is manually removed. Otherwise the system decides.

The question:

Should either of the date inputs allow selecting dates that are in the past?

More specifically, should it be possible to select a start date that has already passed?

Note that we do have validation which will display an inline error message if the end date selected is before the start date, and additionally we present a dismissable warning prompt before saving a piece of content if it will never be active again (i.e. the end date is in the past).