Mint actually can do this, though their method is a bit funky.
Using your example, you set up a $50 budget for phones. In October, you only spend $40. On November 1st, you'll see your budget say "-$10/$50" instead of "$0/$50."
Using another example (with more transactions), let's say you set up a $200 budget for gas, but you only use $150 in October. On November first, you'll see "-$50/$200." The first time you fill your tank up in November, it's only $30, so you'll see on Mint "-$20/$200."
On the one hand, it's nice because it reminds you that you only want to pay $50 a month on phones or $200 a month on gas while still rolling over your remaining budget from the month before. On the other hand, it's not 100% clear exactly how much money you have left in your budget (involves a little bit of basic algebra).
I should note that this isn't the default setting on budgets. You have to edit the budget and check off the box that says "Start each new month with the previous month's leftover amount."
