The BIP32 normal, which is used nearly universally for key/handle derivation, permits as much as 231 (roughly 2.1 billion) keys to be derived inside a single chain.
Usually wallets solely use one or two chains (one for addresses to offer out externally, and one for keys used internally for change), or one or two per handle sort. Nothing prevents wallets from utilizing extra chains than that, however there isn’t a actual want as billions of addresses should be greater than adequate for any particular person consumer (there have solely been nearly 880 million transaction in Bitcoin’s historical past in whole). The place a number of chains are used, it’s for organizational functions (e.g. keys used for distinct functions).
Hypothetically, should you saved creating new chains (from the identical seed even), and saved computing all addresses in every chain, you’ll ultimately generate each legitimate key. You will not see something loop; every generated key will look indistinguishable from random (to anybody not understanding the seed/chain it’s derived from).
Attributable to this random nature, you might want to generate some a number of of the variety of legitimate keys earlier than you’ve gotten an affordable likelihood of hitting all of them. As an analogy, consider throwing balls at a variety of bins, such that every ball lands in a random bin. If there are 10 bins, you will have considerably greater than 10 throws earlier than all bins are more likely to have no less than one ball in it (on common ~29.3), as a result of some will randomly find yourself in already-hit bins.
After ~2264 addresses you’re very more likely to have all keys. For 160-bit addresses like P2PKH and P2WPKH, ~2167 ought to suffice. Observe that these are extraordinarily giant numbers which are unattainable by present computing energy, not even all computer systems on the planet collectively may compute this many addresses in billions of years.