"My dog remembers you."
Translation:הכלב שלי זוכר אותךָ.
Theoretically every noun can take possessive endings. It was very common in classical Hebrew, but in modern Hebrew we almost don't do it at all. For example, if you say כלבי you would sound like a first-grade schoolbook that would have been replaced during the 1980s. :-) But the mechanism is a part of the language, כלבי = הכלב שלי.
Yes, actually, I've recently given it some thought and there are a few leftovers. אחי, אחותי, תורי, לדעתי, זה לא מקומי להביע דעה, אשתי/בעלי/בן זוגי/בת זוגי/אישי/זוגתי.