Happened every once in a while with the runners in the past. Happens occasionally in the UK even today. A couple of years ago a jumper ran in the evening on a Thursday and then during the day on Friday---less than 24 hours rest. The second race was at Ayr and was a four horse field, so he was going get paid as long as he made it around. If memory serves he finished a well beaten second that day.
When the QH/TB fair circuit was active out west, it was relatively common. I remember on horse racing three times in a four day meeting...and the every race was a bit better than the last---the only race it won was the last of the three races.
Depending on the task at hand it is not inconceivable a horse could be fine to go the next day, but in the current climate I imagine few tracks would approve of it.
