Don't think toyota has that warning on their hybrids. Didn't see it on either of mine.
Nothing like that in the manual of mine either. How would the battery get damaged anyway in case of running out of fuel?
AFAIK a Hyrbile Toy Yoda will do three attempts to start the engine in case it has trouble about it, before throwing the gloves down. I doubt Hyundai's system would completely deplete the hybrid battery in order to attempt starting the engine again and again?
However, what my manual does mention about draining the tank is that you must then add enough fuel to have the low fuel warning lamp go away, at least 8 liters, or even more if the car is parked into a hill. Therefore the typical 5 liter spare can is likely not enough to save you from being stranded. So my advice is - regardless what car you have, don't try to do a record between refueling, and don't trust the estimated distance display. It's not a sin to go refueling when the meter show 1/4 remaining!
