This brings up the basic question: How deep a hole can you dig next to adjacent property and not be responsible for holding it up? I know of one municipality that sets the limit at 8 feet.
Another question: How much fill can you place next to your lot line without being responsible for what happens next door?
There is no upper or lower limit. If you effect changes in the adjacent land or structure, a lawsuit will demonstrate the damages that you are liable for. Some exceptions exist with party walls, setbacks, shallow slope fills or cuts.
One problem with fill added to adjacent land can be storm water runoff - this may happen with only a small increase in elevation and get the person adding the fill in "hot water" very quickly.