There are no single English words that meet the criteria. The only 6-letter word you can make with those letters is aerugo.
Luxury, floury, injury, penury are a few 6 letter words that end in -ury
Grouse is a game bird. Rouges are colors applied to one's cheeks. Rogues means a dishonest person.
betake
sexe
Hanger is a six letter word.
the six letter word with e as second letter and 5th is... SECRET jestermeltedbeltedtendertendedmendeddealerheaderLentensedges
GIGGLE
Warble, bawler
novice
Some six letter words with second letter E and ending in ER are:beakerbearerbeaverbeeperbenderbettercenterdealerdearerfeederfeelerfenderfestergendergeyserheaderhealerheaterheiferhelperherderjesterkeeperleaderleanerlecherledgerlenderlettermeanermeekermembermergernearerneaterneuterpeeperpelterpepperpesterpewterreaderreaperrenderrentersealerseekersellersenderserversettersexierteaserteetertellertempertendertestertethervergervesperweakerweaverwelderwelter
blunge, bungle
engulf
littergingerairmenzipperwintersilvermisterringerdieselcitieshiddennickelwickerdiapereitherbilledkidneykilledriskedpiecessigned
Those letters will make the word 'stolen', but you can't make an eight letter word with six letters.