That's a Civ 4 term
In Civ 5 that would be a unit hurried with gold (or faith).
IMHO, it's a good idea to cut a portion of it's health when raised in a besieged city (however, if it's health would be equal to % of the city's health, like Recursive said, that would mean cities with ~10% HP remaining would produce units with these ~10% HP for the same gold price).
Additionally, I'd argue about the need to cut the health of non-hurried units. Firstly, besieged cities are already in trouble building them (due to pillaged / occupied tiles). Secondly, the build process could have started many turns ago, when the city was at full HP...
Finally, I'm not sure the penalties should be applied to faith purchases (holy units), as (unless i'm mistaken) there's always a global cooldown on them.
So, I'd vote for a poll covering all these points
Unless the community has already voted somewhere, and I'm too late with my suggestions.