To begin with, most supervisors are reasonable, decent people. So, the option of communication, depending on the nature of the falling out, is quite reasonable. It is perfectly possible to finish a PhD with a substantially acrimonious relationship. It might be best to study communication skills a bit first.
If that isn't practical, typically, the former supervisor has a lot of power.* However, very few things are absolutes. The purpose of a supervisor's letter is to gain insight from someone who has previously worked with you. In the USA, in my experience, a certain amount of creativity is acceptable as long as you can fulfill that purpose.
For example, my PhD supervisor switched continents and became quite busy with startups without leaving a forwarding address... So, I provided a letter of recommendation from another supervisor along with a note describing the circumstances for some fellowship applications. No problems. Albeit, I worked in research in industry for several years.
*One thing many graduate students overlook is properly researching potential advisors. The cost of a PhD, typically, significantly exceeds the price of a home. And, typically, is much riskier. Yet, somehow, students jump into PhD programs far more easily than they'd buy houses. On the positive side, in departments I have been in, there have been a few supervisors with known personality issues and, within the department, accommodations were made for students leaving those groups.