It's Not Enough to say to a friend, "you know you're welcome to come over and visit any time".
You need to say "Hey, I'd like you to come over for dinner this week. Is Wednesday good for you?"
Maintaining relationships with friends and family is important. Casual 'stop by anytime' throw-out statements are not conducive to that.
It's Not Enough to say to your aging parents, "I'm going to come visit as soon as I have time". You won't have time. You MUST make time. You never know when time will run out.
It's Not Enough to say "let me know if there's anything I can do for you" when someone is going through a terribly difficult time or a loss. For most people, they won't do it. Even if they have a need, they won't call. They don't want to be a burden. When Hunter's Dad's health took this recent bad turn, at first I asked that question to Hunter's mom..."let me know how I can help". Of course she didn't. So I told Hunter to ask her if they would be home on Tuesday night. She said yes. I made dinner and Hunter and I took it over and we all ate together. (except his dad, who is no longer eating.)
Just show up. And if you see a need - offer to help specifically. Don't say "If you need someone to take care of the dog while you're at radiation appointments for several hours, call me". Say "When is the next radiation appointment? OK, I'll be here to take care of the dog."
I don't think there are very many people who sit at a funeral thinking "Man, I spent WAY too much time with this dude. Sure wish I'd made less time for him in my life while he was still living....."