If you run a parity node one of the most important is to check if your sync is running or if it is stopped for some reason. Making sure that the json-rpc is enabled, you can use two checks:
1. Check if the sync is fully synced.
curl --data '{"method":"eth_syncing","params":[],"id":1,"jsonrpc":"2.0"}' -H "Content-Type: application/json" -X POST localhost:8545
if you get a false for the above command, it is fully synced. Otherwise you get the actual block number where the sync stays.
2. Even if it is fully synced, the ancient block sync might be running, so the following command has to show that the blockGap is null:
curl --data '{"method":"parity_chainStatus","params":[],"id":1,"jsonrpc":"2.0"}' -H "Content-Type: application/json" -X POST localhost:8545