That's called "énclisis" (placing the unstressed pronoun after the verb). With personal verb forms apart from the imperative, that's not common in modern Spanish. It was quite common in old Spanish (not only Medieval Spanish, also in the literature from the Siglo de Oro), but nowadays it only exists in some idioms and set phrases and it's also once and again used in literary modern language. But even in literary language its use is sparse, usually to give the language an olde-worlde pompous flavour.
These are the set phrases that come to mind where that kind of énclisis is found in everyday language:
-"¡Habrase visto!" meaning "unbelievable!" (the expression has an énclisis, without it that would be "se habrá visto".
-"Érase una vez..." or "érase que se era..." (once upon a time, there was...), that's the formula to begin a fairy tale.
-"Dícese". Unlike the last two, this is not found in everyday language, but it's a common idiom usually found in dictionary entries (For example, definition of "verde"="dícese del color de la hierba fresca". If you use that expression it makes you sound like a talking dictionary.
Then there is the word "acabose", which is a verb form ("acabose" instead of "se acabó") changed into a noun, meaning "the limit" or "the last straw" (esto es el acabose=this is the last straw, this is the limit, this is the last thing I/we could tolerate/expect/imagine.
Galician, Portuguese and Asturian have their own rules for placing the unstressed pronouns. But not only in their own languages, also in Galician-influenced or Asturian-influenced Spanish spoken by rural people from North-Western Spain (specially rural native Galician or Asturian speakers, more often if they're old) you may still hear some of those énclisis from modern speakers.