Someone who has gone through a major loss will still be dealing with a lot of emotions for years to come. They will also often be lonely and searching for someone to connect with. It's not for everyone and will be a lot of work so please don't fake interest and then drop them as you will do MUCH more harm that way.
If you do have genuine interest then please understand that EVERYONE has some sort of baggage and losing someone you loved dearly is a lot of baggage. However what you gain from that while giving understanding is something you will never experience otherwise. Don't get angry if the name of their loved one who was lost slips out either. It's not done on purpose but shows that they are dealing with their loss and you have likely reminded them of something good that they are missing.
I have personally called my girlfriend my wife's name a couple times on accident and I shake my head and apologize because it's not what I truly meant to say but it's the name my brain reached for in that moment. Sometimes it's hard to deal with but having someone who understands makes things so much easier to deal with.