I came across a sentence:
'The doctor came downstairs and went out to Linda,'
and I was confused by the use of the expression 'go out to' in such kind of way. So far as I know, the expression 'go out to' has two meanings: to be defeated, or to be sympathetic to someone. But the sentence I mentioned used 'go out to' in a different way. Could the expression 'go out to' mean 'reach someone's or literally 'go to someone'?
You are misunderstanding this.
"go out to" is not a specific idiomatic phrase with its own meaning. It mostly means its literal meaning, where "go out" means to move outside and "to" indicates the destination. In this case the meaning is absolutely literal - the doctor goes outside, arriving at where Linda is.
The "two meanings" that you refer to are just two of the many metaphorical usages of "go out". The sense of 'defeat' is from the phrase meaning to exit (go out of) a competition, and where "to" indicates who they were defeated by. So:
Manchester go out to Liverpool in the second round.
"Go out" has its literal meaning of to leave (with an implied object of whatever competition we are talking to) and "to" indicates who defeated them.
In the case of sympathy, "go out" only means that as part of certain specific constructs:
My heart goes out to the victims today
My sympathy goes out to the families of the bereaved
But the meaning is tied up with subject - my heart or my sympathy. "got out to" does not mean sympathetic unless the subject is something that indicates that, like a compassion or sympathy.
Note that in either case "to" is not a key part of the phrase. "go out" carries exactly the same meaning without it.
Manchester go out in the second round.
My sympathy goes out today.
both mean exactly the same thing but without stating who the victorious team are, or who is the recipient of the sympathy.
Without further context I would infer that the doctor came down the stairway, then went out of the doorway to the stairs, into the room where Linda was.
