It depends on the category and training grant restrictions. Sarah is right that you cannot rebudget out of stipends or tuition (participant expenses) without prior approval. Generally I've found that you can rebudget into restricted categories as long as you're still meeting the guidelines of the grant. Example: NIH may award you the following:
$22,920 Stipend
$4,200 Institutional allowance per trainee
$1,324 Other Fellowship Expenses
The funding for "Other Fellowship Expenses" can be applied towards health & tuition expenses because it would be under the capped amount You can't use the "Other Fellowship Expenses" budget amount for the Stipend because the cap is $22,920 on stipend and they awarded the full amount.