Hypothetically, if a foreign company raises money through the US Development Finance Corporation, are they liable to lawsuits in the US if there is a breach of contract between the foreign company and a US person/company?
if a foreign company raises money through the US Development Finance Corporation, are they liable to lawsuits in the US if there is a breach of contract between the foreign company and a US person/company?
Not for this reason.
Possibly, but the question doesn't provide enough information to know.
There are two main theories by which jurisdiction can be asserted over a company in a breach of contract action (which is what is known as an in personam claim seeking a money judgment against someone else, as opposed to an in rem claim seeking to adjudicate rights in a particular parcel of property which is the subject matter of the lawsuit to which different rules apply). One theory is "general jurisdiction" and the other is "specific jurisdiction."
When a court has "general jurisdiction" over a person, it can hear claims against that person arising anywhere in the world based upon any legal theory upon which relief may be granted by a court. Essentially what you seem to be really asking is whether funding through the U.S. Development Finance Corporation gives U.S. courts general jurisdiction over the foreign company.
The answer to this is "no."
The only courts that have general jurisdiction over a company are the courts of the jurisdiction under whose laws it is established (e.g. Delaware for a company formed under Delaware law), and courts of a jurisdiction where a company has a headquarters significant enough for the company to be considered "at home" there (most companies would have only one headquarters, but some companies might have two or three of them that are equally core to its top level operations).
The U.S. Supreme Court adopted this rule in a unanimous 9-0 decision in the case Daimler Ag v. Bauman, 571 U.S. 117, 134 S. Ct. 746 (2014), which overruled a line of cases generally credited to the U.S. Supreme Court case of International Shoe v. State of Washington, 326 U.S. 310 (1945). International Shoe had been widely interpreted for decades, before being effectively overruled by Daimler, to mean that simply having a registered agent in a state, a permanent employee based in a state, or a permanent office for the conduct of business in a state that need not be the company's headquarters, is sufficient to give U.S. courts general jurisdiction over that company.
The facts of the question, however, suggest that the foreign company wouldn't even meet the old International Shoe case standard. Certainly, the mere existence of the funding from a U.S. government agency, in and of itself, would not give U.S. courts general jurisdiction over a foreign company.
The other theory under which a court may assert jurisdiction (in an in personam case like a breach of contract case) is called "specific jurisdiction". This theory requires that the party sued did something to "purposefully avail itself" of the laws of the place where the court is located in connection with the course of events or transaction that form the basis of the lawsuit. Sometimes "specific jurisdiction" is also called "long arm jurisdiction".
So, unless the lawsuit related to the funding transaction from the government agency in some way (e.g. a suit by the agency to collect on a loan from it to the foreign company after it fails to repay the money lent to it as agreed), this funding transaction is not sufficient to establish "specific jurisdiction" over the foreign company.
Instead, the transaction and events that form a basis for the lawsuit would have to have sufficient contacts with the U.S. to justify an exercise of "specific jurisdiction" over the company. A company isn't required to submit to the jurisdiction of U.S. courts for all dealings with U.S. persons simply as a result of receiving this funding.
Domestication of Foreign Judgments
If the U.S. courts did not assert jurisdiction over the foreign company, however, and the U.S. person then won a foreign lawsuit against the funding recipient, the U.S. person could probably domesticate the foreign judgment in a U.S. court (i.e. obtain formal recognition in a U.S. court that a valid judgment has been entered by a foreign court against a person), in order to garnish the proceeds of the U.S. Development Finance Corporation loan that would otherwise have been payable to the foreign person.
Footnote on Tag Jurisdiction
When you sue a natural person, a court can assert jurisdiction of that person (even in an in personam case), if that person has a summons from the court in that case is hand delivered to them in the state where the court is located. This is allowed even if neither the state where the court is located, nor the case, have any other connection to that person. Burnham v. Superior Court, 495 U.S. 604 (1990). This is sometimes called "tag jurisdiction".
But, while the U.S. Supreme Court has not definitively ruled that companies are not subject to tag jurisdiction, the U.S. Court of Appeals for the 9th Circuit (which is an intermediate federal appellate court immediately below the U.S. Supreme Court and covers most of the Western United States) has held that corporations aren't subject to tag jurisdiction, and the U.S. Supreme Court declined to consider a certiorari petition from that ruling. Martinez v. Aero Caribbean, 764 P.3d 1062 (9th Cir. 2014) cert. denied 135 S.Ct. 2310 (2015).