Why is this not throwing a NullPointerException?

null assignments do not change value by globally destroying that object. That kind of behavior would lead to hard-to-track bugs and counterintuitive behavior. They only break that specific reference.

For simplicity, let’s say that sample points to address 12345. This is probably not the address, and is only used to make things simple here. The address is typically represented with the weird hexadecimal given in Object#hashCode(), but this is implementation-dependent.¹

StringBuilder sample = new StringBuilder(); //sample refers to 
//StringBuilder at 12345 

StringBuilder referToSample = sample; //referToSample refers to 
//the same StringBuilder at 12345 
//SEE DIAGRAM 1

referToSample = null; //referToSample NOW refers to 00000, 
//so accessing it will throw a NPE. 
//The other reference is not affected.
//SEE DIAGRAM 2

sample.append("A"); //sample STILL refers to the same StringBuilder at 12345 
System.out.println(sample);

From the lines marked See diagram the diagrams of the objects at that time are as follows:

Diagram 1:

[StringBuilder sample]    -----------------> [java.lang.StringBuilder@00012345]
                                                      ↑
[StringBuilder referToSample] ------------------------/

Diagram 2:

[StringBuilder sample]    -----------------> [java.lang.StringBuilder@00012345]

[StringBuilder referToSample] ---->> [null pointer]

Diagram 2 shows that annulling referToSample does not break the reference of sample to the StringBuilder at 00012345.

_{¹GC considerations make this implausible.}