You will need to consult with an experienced transaction lawyer on this, to ensure that you are not opening yourself up to lawsuits in another country and that country's legal system. If you have a dispute over the quality of work or the price, even a small contract can become a big headache, if you are sued in a foreign jurisdiction for unpaid contract amounts. It is unclear what you mean by "report them." If you pay for services in advance and they don't provide the goods when promised in proper condition, expect to need an experienced lawyer to handle the case for you.
Robert Stempler (please see DISCLAIMER below)
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Mr. Stempler did a very good job of answering your question. You also asked "Is it a bad idea to outsource work to people in a different country?" If they do a good job for you, then it may be a very good decision. However, if they do a bad job, then you will probably have a harder time trying to recover for any damages you may incur. Good luck.
*Scott G. Nathan has been licensed to practice law in California since 1983. The information presented here is general in nature and is not intended, nor should it be construed as legal advice for any particular case or matter. This posting does not create any attorney-client relationship with Scott G. Nathan or my law firm. For specific advice about your particular situation, you should consult with an attorney immediately.
Of course, it depends on the country and the individuals involved. Generally, the answer is no. The exception would be those companies with assets in the US or those willing to post a performance bond or some other type of security (which is very, very rare.) Some of our biggest trading partners have no legal system of use to Americans - e.g. China and Mexico.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
I would need to know a lot more information about the type of business you are in and how the vendor fits in as part of it. For example, it it is a software developer writing code for you vs. An assembly company shipping you completed products the risks and issues are completely different.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.