knowing no bounds; showing no signs of stopping
Set phrase used to describe something that continues relentlessly, often in a negative or overwhelming sense (e.g., inflation, ambition, violence).
His ambition knows no bounds.
The rise in prices shows no signs of stopping.
限りない means 'limitless' or 'infinite' as an adjective, whereas とどまるところを知らない is a verbal phrase emphasizing relentless, often negative, progression.
Kana spelling is common for this set phrase; the kanji forms are also used but less frequent.
Kanji spelling using 止 (stop).
Kanji spelling using 留 (stay/remain).
A set phrase combining とどまる (to stop/stay) + ところ (place) + を (object marker) + 知らない (does not know), literally 'does not know a place to stop'. The exact origin is uncertain, but it follows a classical Japanese pattern of idiomatic expressions.