Thrown object cannot be caught in a multi-threaded solution

I have a RAII class that solves a problem in an inner thread:

#include <iostream>
#include <thread>
using namespace std;

struct solution_using_thread {
    solution_using_thread()
     : alive_(true), thread_() {
        thread_ = thread([this]() {
            while(alive_);
        });
    }
    ~solution_using_thread() {
        alive_ = false;
        thread_.join();
    }
private:
    bool alive_;
    thread thread_;
};

int main() {
    cout << 0 << endl;
    try {
        solution_using_thread solution;
        throw 1;
    } catch (int i ) {
        cout << i << endl;
    }
    cout << 2 << endl;
}

After creating an instance of it, the main happens to throw an exception. The problem is in some of the executions, the output is:

0

when it always should have been:

0
1
2

In coliru, it is always only 0.

What am I missing here?

PS: Sorry, for the ambiguous title. Please do not hesitate to suggest a better one for this question.