I bought my arba minim and had the rav on site check them. The stem on the esrog seemed wet, but he said it was fine and still mehudar alef alef (it was sold as a closed box, so there wasn’t an option to swap it). However, when I opened the box at home the stem had completely fallen off. As far as I know, this makes the esrog pasul lbracha for the first day. I saw someone quote a teshuva that there is a kula to glue or otherwise reattach it since it is pasul because of hidur and not being “lacking.” Is this an accepted practice?
Unfortunately you can not glue it back in. The overwhelming majority of poskim say that this can not be done, and even though there is an opinion that does say this, it is definitely not the accepted practice, and it is only meant from the second day. In fact if we will say that it is a lacking in hiddur, it would make things worse, because then it would be pasul for all seven days.
O;CH 649-8, Eliyahu Rabba 648-14, Svus Yackov1-35, Binyan Tzion – 40, Bikurei Yackov 648-26, Sharei Teshuva 648-16, Dovev Meisharim 1-80, Divrei Malkiel 1-33, Chaim Ubracha 244, Maharsham 7-94, Mishneh Halachos 15-195, Simchas Yisroel 33-22. Ashrei Ish chap. 31-3. Orchos Rabeinu 2 pg. 278,