How to Handle SIGABRT signal?

As others have said, you cannot have abort() return and allow execution to continue normally. What you can do however is protect a piece of code that might call abort by a structure akin to a try catch. Execution of the code will be aborted but the rest of the program can continue. Here is a demo:

#include <csetjmp>
#include <csignal>
#include <cstdlib>
#include <iostream>

jmp_buf env;

void on_sigabrt (int signum)
{
  signal (signum, SIG_DFL);
  longjmp (env, 1);
}

void try_and_catch_abort (void (*func)(void))
{
  if (setjmp (env) == 0) {
    signal(SIGABRT, &on_sigabrt);
    (*func)();
    signal (SIGABRT, SIG_DFL);
  }
  else {
    std::cout << "aborted\n";
  }
}    

void do_stuff_aborted ()
{
  std::cout << "step 1\n";
  abort();
  std::cout << "step 2\n";
}

void do_stuff ()
{
  std::cout << "step 1\n";
  std::cout << "step 2\n";
}    

int main()
{
  try_and_catch_abort (&do_stuff_aborted);
  try_and_catch_abort (&do_stuff);
}