Usually used in formal English for strong anger, grief, hostility, or demands that cannot be softened by apology or persuasion. Common both before a noun and after verbs such as be, remain, and become.
常見錯誤
The unappeasable rain kept us inside all weekend.
The relentless rain kept us inside all weekend.
'unappeasable' is used for people, feelings, or demands that cannot be calmed, not for weather.