“Masochistic Tenshi” is an old, yet plausible, Touhou Project fan theory claiming that, with the release of Touhou Hisouten in 2008, there's hints suggesting that Tenshi Hinanawi is an “extreme masochist” (ドM). However, it hasn't received any definitive confirmation in canon.

In Touhou Hisouten, we have Tenshi admit that she caused the incident, as she was bored, and encourages Reimu to “eliminate” (退治) her. Furthermore, her “State of Freedom from Worldly Thoughts” (無念無想の境地) spell card informs us that she was actually using kiai to endure the pain. This was later revisited in The Grimoire of Marisa, where it's given a unique “Masochist Level” (マゾ度, Mazo-do) of 5 stars.

While a solid argument, this is not a definitive confirmation of Tenshi being a masochist. Naturally, some fans ran with the idea: abusing her, pairing her with alleged sadists (e.g. Sanae, Yuuka), and giving her a study body, which explains why some fan-made RPGs may give Tenshi a high defensive stat. Once again, it isn't set in stone, so be mindful that some fans may embrace or reject the theory.

• It has been tentatively called “Most Masochistic Princess” (モーストマゾヒスティックプリンセス) and “Ultimate Masochistic Creature” (アルティメットマゾヒスティッククリーチャ), but these are rarely used and there isn't a general consensus on what it should be called.
• The IOSYS doujin circle released an arrange that was titled “Uchouten Mazohisutikku” (有頂天マゾヒスティック)¹⁾ in their 2008 “Touhou Bubbling Underground” (東方泡沫天獄) album.

• Sadistic Sanae
• Ultimate Sadistic Creature - Arguably boosted this fan interpretation.

• Most Masochistic Princess on Pixiv Encyclopedia