質問: 甲斐{がい} seems to have the property where it conjugates with the 連用形 of verbs unlike most nouns with which verbs typically attach with the 終止形. i.e you say 生き甲斐 instead of 生きる甲斐, やり甲斐 instead of やる甲斐. I imagine this is due to some relic of older Japanese, but I'm unsure what it is. Thinking about it a bit for some other nouns that might do this, it seems that 損 might have this property as well. Is there a name for nouns that work like this? And are there some other examples of nouns that do this?
回答: How about 「接尾語になる名詞」 or 「複合語の後ろの要素になる名詞」, perhaps? 「教える[甲斐]{かい}」「教え[甲斐]{がい}」 「困ること」「困りごと」 「サボる[癖]{くせ}」「サボり[癖]{ぐせ}」 「置く場所」「置き場所」 「行く場」「行き場」 「送る先」「送り先」 「帰る道」「帰り道」 「食べる[時]{とき}」「食べ[時]{どき}」 「食べる物」「食べ物」 「座る順」「座り順」(← probably colloquial. maybe only used in Kansai?) 「死ぬ[様]{さま}」「死に[様]{ざま}」 etc... ??