Think how you would re-act/act in that situation and you will have your answer Caro. But there is no golden rule that can apply to every immigrant and how an immigrant behaves in a new country is entirely dependant on the attitude of the individual and for variety of very different reasons.
The situation in the native home, the experiences of the immigrant in his native home, the reason for immigration, the personality of the immigrant, the situation in the host country and the attitude toward outsiders in the host country all play a part in how an immigrant adapts to and behaves in his/her new enviroment.
It is also worth noting that the majority of immigrants leave home with the intention of returning. In my experience, these are the immigrants who tend to cluster together in communities. But returning home also becomes increasingly difficult as time goes on and again for a variety of different reasons. People change in a new enviroment, they become settled in home and work, their children are part of the new country and not the old, whether they intend it or not an immigrant does become involved in or part of a wider community and as the immigrant himself has changed so has the native country and maybe not in a beneficial way. All this and more can and does play a part, so whilst an immigrant may leave with the intention of returning, it is usually only a minority that can actually make the transition back after living away for many years.
Yet some immigrants leave home with the realisation or intention of not returning home to live and they are generally the people who will immerse themselves fully in a new culture and adapt to a new life far more readily than the former.