How to apply a block cipher to (large) packetized communication when packets can get lost/erased?
Is it really just a block cipher in ECB mode, so that each packet can be decoded without any prior packet⁰?


No. ECB is bad and creating a secure real-time channel (that can even handle packet loss) is a solved problem. It has been for years. There's no good excuse for using ECB here.


  Is it a block cipher in some non-ECB mode, but it gets reset at the start of a packet?


The usual approach would be to have some form of initialization vector for the encryption which is sent as cleartext with every packet and is used to re-synchronize the state between both endpoints if packet loss is expected. For some encryption schemes this can simply be the packet counter. Then once you have synchronized state for a packet, you use a stateful encryption scheme, like GCM or CTR + HMAC to encrypt the singular packet.

If you want to have a look at how this works out in practice, the three big secure channel standards are TLS (cannot handle lossy underlying layer), DTLS (adaption of TLS 1.2 for lossy contexts) and SRTP.