I will probably get censored for this but....I did it for my MIL with total and complete deception. I guess this strategy depends on how advanced the person is with their illness, whether they will see through the outright lies.
This is what I did: I told MIL we were going out for a coffee. Suitcase (pre-packed) was hidden in boot of car the night before. We walked into the care home together and straight into the lovely garden, where other residents were enjoying morning refreshments. We sat at a table and were given coffee by one of the staff. After a suitable amount of time, I excused myself for a toilet visit. But I didn't return - instead I legged it out of the home and into the car park. Suitcase was dumped in the reception area (out of sight of the garden where she was sitting) and I drove home as quickly as I could. I didn't visit for at least a week afterwards.
By the time I did visit, MIL was delighted to see me and had absolutely no recollection of how she had arrived at the home. One year on, she is still there (permanently), and is safe, well, and kept entertained by numerous activities.
I'm not sure that I should be recommending such a deceitful approach -I'm not proud of it - but it worked at the time, thankfully with no lasting ill-effects!