Not sure if this answer will help you; it is focused on boxing and kickboxing. But I do think that this is a good question, particularly because access to gyms (and partners) are limited due to social distancing. A lot of people may have this question and may benefit from this answer.
First, there is absolutely no equivalent of "partner work" (i.e., pad work, drills, sparring, etc.). But there is something more we can do other than shadowboxing (and bag work for those who have a heavy bag at home) to improve our skills, speed, technique, endurance, vision, etc.
Virtual Pad Work and Virtual Sparring
I have been following a Youtube Channel called "Precision Striking" by Jason Van Veldhuysen (= the coach) for a long time. This guy is just unbelievable; he is a great martial artist and a phenomenal coach. He has these virtual training videos where he will hold pads and call out combos that you need to throw. Basically, you stand in front of your computer and do very creative virtual drills. There are three types of virtual training videos: Pad work, Defense drills, and Sparring. The "defense" and "sparring" videos will help a lot with head movement, blocking, parrying, counter punching, and seeing more punches — of course, you have to do it seriously like you would with a real partner. There is music and sound effects to help you with your combo-timing.
Here is a simple combo: Jab, Cross, Hook, Cross (1-2-3-2)
Here is something from one of his virtual sparring videos. Note how his camera moves too when he attacks and moves — so you have to move too during the exchange (it will help with movement and footwork).
Precision Striking: Virtual Boxing Simulation
There are a bunch of these virtual training videos in that link. Here are some that I have used:
- Interactive Boxing Home Workout #1 (Pad Work)
- Defending the Right Hand | Visual Reaction | Virtual Sparring
- Virtual Boxing Sparring in 4K
There are a few other things you can takeaway from this. You can record yourself (or ask a friend to record themselves) holding pads for kickboxing and calling out some interesting combos. This will allow you do add in elbows, knees, and kicks. You can then use that recording in the same way. You can also do this over Skype/Zoom with a friend in real time.