Do you think it is possible to lose weight and stay physically fit without reciving proper nutrition

I don't think it is possible.

Explanation:

You can loose weight by not consuming anything (not receiving proper nutrition) and it can be damaging to the body. Also without the proper nutrients is would be hard to maintain fitness because you would lack energy and could get more cramps.

Starving (another way not to get nutrition) to lose weight makes your body more likely, in the long run, to replenish fat. It uses the new basal metabolic rate from starvation mode. Lean individuals were more likely to gain more fat after starvation

to provide benchmarks