According to the Lovin Malta Maria Efimova applied for a political asylum in an unknown country. Can a country provide asylum to a person from a friendly country even though the actions of the person might have been correct? Doing so may perhaps harm the relations between the two countries.
Yes, it can happen.
One example is Denise Harvey, a citizen of the USA who was given asylum in Canada in 2014. Harvey had been convicted of having sex with a 16 year-old boy, which was a crime in her home state of Florida but not in Canada:
Her request for protected person status was heard by the Immigration Review Board (IRB) in July of 2012 and the IRB granted her request because it agreed her sentence was indeed cruel and unusual punishment and the crime she was convicted of is not a crime in Canada.
The USA and Canada continue to be close allies and trading partners; there is no indication this case had any significant impact on their relationship.
Obviously, a more politically charged case such as that of Julian Assange may have implications for relations between the countries involved. But the host country is still free to grant asylum, and accept the consequences to its international relationships.