There are a number of churches which claim “Old Catholic” Apostolic Succession or some other similar scenario. These have proliferated widely over the last 130+ years or so.
Are there some few of these Apostolic Successions which are “valid or probably valid, but illicit”? Yes. The vast majority? No.
Some were formed for political reasons (whether for good or for ill!) (The Polish National Catholic Church, some of the South American schismatic bodies).
Some were formed by rejecting the Holy See for “liberal” reasons (The Old Catholic Church – in its original iteration!; more recently for reasons having to do with disapproval of Catholic moral teaching.)
Some were formed by rejecting the Holy See for “conservative” or “traditional” reasons (SSPX – though their case is quite different; some of the South American schismatic bodies.)
Many, if not most, of what proliferates today, trace their “lineage” through one of two very questionable sources who drifted in and out of the “Old Catholic” movement. Much of what has devolved from those bodies, ie, the “Liberal Catholic Church”, the "Church of Antioch (Spruitt), etc. are more theosophical and even gnostic than Christian (even in the most liberal sense of the word.)
Hope that this helps . . .