Someone who is moving is so out of sorts with things all over the place in their lives, they might need a break. Since they need to be doing all the things at their house offer them to come to your house for a coffee or tea break. They will know they can leave whenever they need to and you will understand. Make that known to them as soon as you tell them your invitation to come for a beverage break. If they cannot come the day and time you offer, keep on inviting them so they can accept your welcoming idea.
You know the person is busy moving, so make your phone call short. This allows the person to get back to working on moving without being curt to you. Give them a call and tell them you are able to help them certain days and hours so they can call you if your help is needed and wanted. Some people have lots of family doing the jobs, but it is so nice to get a call from a person who wants to be a helper when you are moving. In a few days, give them a follow up call to tell them you will miss them when they move.
If you know the person who is moving has a dog or cat, offer to help them with the care of the pet when and if you can. If they want you to take the dog to the groomer or day care, you can offer those helps too. A cat can simply come and remain in your home for a few hours while the doors of the person moving are wide open for the movers to come and go. Animals get nervous when strange things happen and your offer to take care of a pet will be most welcomed for one or two days.
When a person is moving, sometimes they don't know where they have put their dishes or pots for cooking meals. Offer to bring in a dish for them when you want to help them. Bring in paper plates, utencils and napkins so they do not have to find their things they have already packed away. Find out what limitations people have for their diet requirements so everyone can eat what you help with your dish that will be delivered. Follow up with a return visit to collect your utensils and dishes you served your meal on when you brought food to them.
There are some last minute things that people who are moving need help with that you can do for them. It might be something like contacting the garbage service to pick up the containers. Find out from the people who are moving what they need you to do that you are willing to help with in a sincere way. You can make a list of things you think you can offer if they say they don't need any help in any way. The list you prepared might give them some ideas that they can take you up on doing for them.
select one here...