Learn French: Il s'attache à elle, même si elle est loin. - He is getting attached to her, even if she is far away.

Normally, to say "to her," you would use the indirect object pronoun lui placed before the verb. However, s'attacher is a pronominal verb (it has that reflexive s'). French pronominal verbs that take à do not allow you to use lui or leur for people. Instead, they are "non-cliticizing," meaning you must leave the preposition à after the verb and follow it with a stressed pronoun (like moi, toi, lui, or elle).

If he were getting attached to a place or an object, would we still use a stressed pronoun?

No. The rule about keeping à and using a stressed pronoun applies to human beings. If he were getting attached to a new city, a project, or an idea, you would replace à + [thing] with the pronoun y. It would move in front of the verb: Il s'y attache (He is getting attached to it).

I see même si (even if) used with the indicative (est). Shouldn't expressions of concession trigger the subjunctive?

It is a very common trap! While similar expressions of concession like bien que or quoique (although) strictly require the subjunctive, même si is an exception. It always takes the indicative mood, so you treat it exactly like a regular si (if) clause.