Strange is likely alluding to the prospect of having his heart broken, which is a risk that comes with falling in love with someone, since you may ultimately lose that person for one reason or another.
From Wikipedia:
A broken heart (also known as heartbreak or heartache) is a metaphor for the intense emotional stress or pain one feels at experiencing great loss or deep longing. The concept is cross-cultural, often cited with reference to unreciprocated or lost love.
Failed romantic love can be extremely painful; people with a broken heart may succumb to depression, anxiety and, in more extreme cases, post-traumatic stress disorder.
From The Free Dictionary:
broken heart
What one is said to have when they are very sad, typically due to a tragic event or the end of a romantic relationship.
When my girlfriend dumped me, I thought I would die from a broken heart.
Well, my son is dead, and I feel like my broken heart will never heal—that's how I'm doing.
Ah, you recently ended a relationship too. So there are two broken hearts here today, huh?