A spacecraft capable of supporting multiple generations could permit the pioneer's descendants to complete the journey. Don't think anthropomorphically, maybe THEY live 100,000 years and would consider a 1000 year journey feasible. But, would such a trip be worth the cost. This missions described above would require resources equal to the GNP and energy budget of the United States for decades. Speculative physics could make such journeys feasible.
Time passes more slowly for a traveller moving at nearly the speed of light.
Our current understanding of physics is quite limited. We've only been at it for a few hundred years. THEY may have been at it for billions of years.