Two articles about fossilization from wiki are:
But especially first one is stub. what are all meaning of this term in linguistics and applied linguistics?
Fossilization is a metaphor. What it means in paleontology (the source context) is the very rare gradual replacement of normally degradable biological material with non-degrading material. Typical is animal skeletal material replaced with rock, as in dinosaur digs (fossil means 'dug up' in Latin).
In any linguistic context, this metaphor theme projects the dynamic aspect of something active becoming gradually less active and retarding change. Part of the DEATH frame, probably. The rocks are not necessary.
In historical linguistics, fossils are the non-productive but still detectable traces of vanished paradigms and syntagmas. These are not discovered as rocks, but as old junk still attached to some words, like fragments of plastic packing might adhere to a toy.
In 2nd-language-learning terms, fossilization is the fixation of a given speaker at a certain level of competence in a foreign "interlanguage" -- interlanguage means what people actually learn as adults when they acquire a new language. Interlanguage and fossilization are coinages by my colleague and former teacher Larry Selinker.
The Interlanguage theory essentially says that people get better and better at a language until they get good enough for their own purposes, and then they don't get much better after that. This is called "fossilization" at some level of competence, and the metaphor is one of gradual cessation because of inactivity, although what's being turned into a fossil is just the person's inclination to learn novel words and constructions in a language.
This is the meaning I'm more familiar with. Fossilization, in this case, is a diachronic process (happening over time) within a single language.
Patterns within languages can be productive, like adding -s to nouns to make them plural in English, or non-productive, like adding -en to nouns to make them plural. Both are used: cat → cats, ox → oxen. But a productive pattern can still be applied in completely new cases, such as wug → wugs, while a non-productive pattern won't: no native English-speaker would see the invented word wug and pluralize it as *wugen.
Fossilization is when a productive pattern stops being productive, but leaves some traces behind. In English, the plural in -en is no longer productive, but still appears in oxen, children, brethren, and a few other words. So the pattern, and those words in particular, are now said to be "fossilized".
I'm less familiar with this usage, so please correct me if I get any part of it wrong. But "fossilization" can also refer to something that happens in language-learning, when traits of the first language "stick around" into the second.
For example, a native speaker of English (which has an SVO word order) might keep applying that word order in Japanese (which instead uses SOV). The SVO word order is then considered a fossilized trait: it's not proper Japanese, it's just a relic of them previously having learned English.