I used to believe that the following is correct:

"He suggested (that) she (should) leave."

"that" and "should" are omitted, so the usual
way of saying it is:

"He suggested she leave."

but someone in this forum said "should" shouldn't
be there. If it's true, then why it's not

"He suggested she left."

Is there any grammatical rule behind it?

Also, how about words with similar meaning like
"recommend" and "propose". Do they follow
the same rule?
He suggested she should leave

referred to an action that (at the point of time when he suggested) should happen in the future. "Should" has to be here because it determines the modus of the verb leave (here: she should go - it would be better if she went).

Another possibility could have been "He suggested she left"

this refers to an action (at that point of time) that has happened. She obviously has disappeared so he suggested that she left.
I used to believe that the following is correct:

"He suggested (that) she (should) leave."

This is a subjunctive thing. Like, there's no "should" in "I suggest you leave", and to put one in would be a mistake, because it's not future tense, it's present tense. Also, "should" implies obligation - "You should be nice to people" means "You are supposed to be nice to people", whereas "I suggest you be nice to people" (Note "be", not "are") is a very, very strong suggestion. Almost an order, in fact. But definitely not a reminder of an obligation.


1. "she should leave" -- Implies she has an appointment or something
2. "she leave" -- Implies you want her to go

It's hard to suggest that someone have an appointment or something, so the "suggest" doesn't go well with "should". Same goes for "recommend" and "propose".

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So I suggest or suggested or am suggesting that she leave ......
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I recommend that he BE promoted as an executive in this department.