I can't really understand your post. A bit more detail might help.
To try and answer what I think you mean, it could be that the drain from your bathroom sink goes into the wall and connects into what is known as an "internal stack". This is a large diameter (~ 4 inches) pipe that all the drains from sinks, bath and toilet feed into. This then goes into the main sewer connection to your house.
Alternatively, since you say it's not a closed pipe, it may be that it goes through the wall to the outside of the house then feeds into a hopper in the rainwater drain from the roof gutters. That's what mine does.
Newer properties tend to have the internal stack arrangement whereas some older houses use the rainwater drain line for waste from sinks and baths, but not toilets as these have to be connected directly into the sewer system.
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