Well on my opinion I think that an engine failure should be avoided at all costs, even though most flying schools have really old battered and worn out aircrafts which will still be used. But if you have an engine failure at low altitude such as 6-900ft I would just ignore the transponder and just give a breif small radio call with a mayday and your callsign, as they would know where you are. And just land the god damn thing on the best thing you can find, such as a nice green field which we all love to see. If you have altitude lik 1500ft to 2000ft then you can do a short circuit and land back on the runway, as most airports such as kissimmee airport in US don't have clear green lands for quite far away, so instead if there was an engine failure you would be going into the town centre or buildings. But do all your checks properly and fly the plane properly as if it was your baby then nothing should really happen.
BRI ^^