This is not the entire truth, and figuring out some of the complications with regards to its reference deserves a post of its own.
It can in fact also refer to objects, indirect objects as well as any head within a noun phrase under certain circumstances. In the latter case, the reference is fairly unambiguous - except that prepositional attributes can be ambiguous with adverbial prepositional phrases. In cases of object or indirect object reference, the reference may sometimes be ambiguous.
Finally, there are cases where the reflexive pronoun refers to some non-existent argument, such as an implicit agent of an infinitive.
I will not present the case when it refers to the subject.
The reflexive possessive pronoun will be "sy" throughout this, by analogy:
sin : sy
Elin visade Per till sitt nya kontor.
Elin showed Per to sy new office.
For many Swedish-speakers, reference to the object here is perfectly fine. It does become ambiguous, but you can find some speakers who think 'hans' (his) is wrong in this context, and others who think 'sy' is wrong in this context.
2. Objects that are subjects of infinitives
Mamman lärde pojken att stryka sin skjorta
The mother taught the boy to iron sy shirt
For most Swedes, the shirt here would be the boy's, but the construction is somewhat ambiguous. "Hennes" (hers) for reference to the mother may be considered wrong by some speakers.
3. Absent subjects of subjectless infinitives
Att känna sina gränser är viktigt.
To know sy limits is important.
4. Heads of NPs, (sy in adpositional attributes)
Sven läste inte boken i sin helhet.
Sven did not read the book in sy entirety.
The rule that normally is bandied about - that sy refers to the subject - would make 'sy' here refer to Sven. However, pretty much every swede understands this as referring to the book, and this kind of expression are very common in all registers of Swedish, including academic, literate, poetic and colloquial speech.
5. Beliefs about 'sin' among speakers
Many speakers believe that 'sin/sitt/sina' unconditionally refer to the subject. Many of these parse other constructions correctly, use them frequently, but correct them whenever they are made aware of them. This is probably because teachers have taught them an excessively simple rule - viz. that it refers to the subject. For over a century, grammarians have been aware of the complexity in reference for 'sin/sitt/sina', and every serious grammar of Swedish accounts for this. It is shameful how many Swedish grammar nazis tend to be ignorant of this, and I find them to be laughably ignorant, to be entirely honest.
This post is meant to show that a feature of a natural language oftentimes is both more complex than the most common description of it -viz. "reflexives refer to the subject", - and also note how speakers sometimes have conscious ideas of how their language works that differs from how the language works and from how they actually use it.