Never seen before C++ for loop

The condition of the for loop is in the middle - between the two semicolons ;.

In C++ it is OK to put almost any expression as a condition: anything that evaluates to zero means false; non-zero means true.

In your case, the condition is u--: when you convert to C#, simply add != 0:

for (u = b.size(), v = b.back(); u-- != 0; v = p[v]) 
    b[u] = v; //                     ^^^^ HERE

Lots of accurate answers, but I think it's worth writing out the equivalent while loop.

for (u = b.size(), v = b.back(); u--; v = p[v]) 
   b[u] = v;

Is equivalent to:

u = b.size();
v = b.back();
while(u--) {
   b[u] = v;
   v = p[v];
}

You might consider refactoring to the while() format as you translate to C#. In my opinion it is clearer, less of a trap for new programmers, and equally efficient.

As others have pointed out -- but to make my answer complete -- to make it work in C# you would need to change while(u--) to while(u-- != 0).

... or while(u-- >0) just in case u starts off negative. (OK, b.size() will never be negative -- but consider a general case where perhaps something else initialised u).

Or, to make it even clearer:

u = b.size();
v = b.back();
while(u>0) {
   u--;
   b[u] = v;
   v = p[v];
}

It's better to be clear than to be terse.