That which we say an Avel (person in mourning) is among the people that need "shmirah" (Someone to be with them - See Gemorah Brachos 54b at the bottom) is this also on Shabbos? Normally we say that Yisael doesn't need "shmirah" on Shabbos since the Shabbos itself protects them.
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The SA HaRav in OC Siman 267 Sif 5 writes that we don't end of the bracha of "Hashkivanu" Friday night (before Shemoneh Esrei) with the ending "Shomer Amo Yisrael" like we do during the week because Yisrael (as a whole) doesn't need "Shmirah" on Shabbos. The Shabbos itself is what "guards" us. However he does say at the end of the sif that a Yachid does need Shmirah on Shabbos.
From here we could say then that those mentioned in the Gemorah in Brachos Daf 54b that need "Shmirah" would need not only during the week but also on Shabbos.