Does a decrease in wealth cause a movement along or a shift in the consumption function?
A decrease in wealth will cause a shift in the consumption function, not a movement along it.
The consumption function shows the relationship between disposable income and consumer spending. It tells us how much consumers will spend at various levels of disposable income. Therefore the only way to move along that function is to change disposable income.
A decrease in wealth will cause a shift in the function because it will make people less likely to spend their income. If I have a great deal of wealth because the stock market is high, I am more likely to spend my income. If I lose wealth because the stock market crashes, I will feel less secure and will be less likely to spend my income.