After losing network connectivity to NTP servers, ntpd or chrony will continue to run. Clock discipline will continue based on known trends. Reach statuses reported for each peer will decrease when packets do not arrive on schedule.
How fast this diverges from stratum one mostly depends on if drift was recorded from earlier NTP packets. Paul Gear's local only experiment shows a server with only a drift file slowly deviating from a host with enough NTP sources. Remove the drift file, and the much worse deviation shows how bad the server's local clock is.
Do not use undisciplined local clock, aka refid LOCL, aka 127.127.1.0. Not appropriate for a client ntpd that is not serving time. For running your own NTP service, multiple peer servers at the same stratum, orphan mode is better.