The unfinished frames and radiant matrices will get removed from inventory at every weekly reset. This has been since update 2.1.4 (January 2019).
[quote][b]Weapon Frame Updates[/b]:
- Ballistics Logs no longer removed at reset
- Ballistics Logs increased cap to five per character
- Ritual Frame quests carried across reset now “refund” into purchased currency
- “Gold” frames refunded into one Ballistics Log
- “Silver” frames refunded into three Modulus Reports
-Any instance of a “Radiant Matrix” removed on weekly reset[/quote]
https://www.bungie.net/en/News/Article/47595