sieve tubes of phloem lose their nucleus at maturity state. still remains alive. how?

Sieve tubes are long, tubular structures. They are living cells but have lost their nuclei to become specialised for the translocation of food. Its not that the sieve tubes do not have nucleus. They develop initially as cells with nuclei but as they attain maturity, they lose their nucleus completely. This is an adaptations for its function to translocate the food. 

Hope this helps!