Vazgeçilmezimsin.

It is understandable but is it well-formed?

Yes it is.

vaz geç-il-mez-im-sin

Ok, it´s just that

- the logical object of vazgeçmek is you

- the verb is passivized > you become the subject

- still, there is the possessive suffix -im which indicates that the logical subject of vazgeçmek is me.

Quite a complicated way to come to the goal.

Thanks gokuyum.

So does it mean something like:

You are my not-to-be-given-up-on ?

Like: You are something that I won´t ever give up on?

I wonder how does this word "feel/look like" for Turkish native speaker? Is it something completely natural, or something more like wordplay? Or maybe both? Or none?

It doesnt sound natural. It sounds fancy and poetic.

vazgeçmek (to abandon)

vazgeç+l(passive)+me(negative)+z(negative present simple)---->vazgeçilmez (one can´t abandon) / (direct: unabandonable, disabandonable)

vazgeçilmezim (my favourite (my disabandonable))

vazgeçilmezimsin (you are my disabandonable (direct: you are the one whom I can´t abandon))