Note : Just some raw ideas here
What does it mean to ‘contain conflict within national borders’ ?
It could mean that news of the conflict is not spread to other countries.
It could mean that direct or indirect manifestations of the conflict do not take place in other countries.
So, is it possible ?
1) No. In the age of the internet and social media, people outside the conflict zone can begin taking sides & even try to affect change within the conflict zones (e.g. Palestinian issue : the BDS movement has picked up steam with government and non-government actors moving against Israel)
2) No. The region cannot be stable when any one country suffers from conflict. (e.g. Turkey, Jordan, taking in refugees from the Syrian crisis & Chad, Egypt, Congo accepting Sudanese refugees fleeing Darfur)
3) No. Foreign allies become potential targets (e.g. foiled attempt at bombing the MRT station in Sg. Sg is seen as a target by extremists because of its position as a US ally). Alternatively, there is always a chance of proxy wars (e.g. Russian entry into the Syrian fray has been dubbed a proxy battle to counter US meddling in the Crimean crisis in Ukraine)
4) No. Because of universal values for humanity, especially those promoted by the United Nations, countries with the ability to intervene may feel compelled to raise the conflict to become an issue of international concern.
5) No, especially not in the case of terror threats where recruitment from other parts of the world is actively carried out. Governments then have to move to protect their own citizens.
6) Depends on the scale & type of the conflict. Some matters are not significant enough to get the attention of people in other countries.
7) When there is enough censorship and sufficient controls, news about a particular conflict may be limited. The rest of the world may know little about it.