Learn English – May I write”…they been so kind and arranged “

You're looking for any of:

"This had been checked and then sent to you." or

"This had been checked before it was sent to you." or

"This had been checked before [I, s/he, they, Sally] sent it to you."

Either there needs to be a subject for "send" (whomever is did the sending) or that part also needs to be in the passive voice. And since the sending happened in the past, it needs to be in the past tense ("sent").

BE come on the analogy of BE gone is a good guess, and in fact in older English it was usual to use BE rather than HAVE to form the perfects of verbs of motion; but this is no longer idiomatic in Present-Day English.

Gone in "He's gone now" is what is sometimes called a deverbal: a participle that has been recategorized as an adjective. Some others are

• done
• excited and exciting
• experiencing
• finished
• interested and interesting
• surprised and surprising

You pretty much have to learn one by one which participles can be used as adjectives, and in what contexts: some can be used as predicate complements, some as attributives before the noun modified, some can be used both ways.