that is not possible.
you have to give something to receive something in return.
for example you have to spend your computing power and mine some coin to contribute to its hashing power and make 51% attacks harder.
or you have to invest your money and buy some altcoin to have a share of it to run a PoS node and earn stakes.
you can run a full node of some coin, like bitcoin full node and contribute to its network and increase the decentralization of it a small amount but you won't be earning anything.
Thanks for the tips!
I see two tasks in front of the network:
1. To complicate the replacement of blocks (mining is used for this).
2. Contain full nodes.
I think that the wrong decision was chosen in Bitcoin, in which only miners receive a reward.
At this moment, I have two full node of Zcach and Monero, which loads all my 4 real cores of processor (i5-4690), uses 8GB memory, SSD- disk and high-speed Internet (~4 MB/sec). Perhaps there are coins, where it is at least somehow rewarded.