I am a landlord and not a lawyer. I will be answering from that perspective. As well, I can only answer based upon U.S. law and the laws in the states where I am licensed and bonded.
I am working off of "I want to rent the place, let's sign a sublease." There is little other information to assess the situation fully.
"I want to rent the place, let's sign a sublease." in of itself is not enough to constitute an agreement. For an agreement to occur, and therefore be enforceable, there must be a meeting of the minds. This would require responses back and forth with specific details being discussed. For example, "I would like to move in on Wednesday." and a response something similar to "You can move in on Wednesday. I have some paperwork for you to sign and I have to give you the keys." The statement "I want to rent the place, let's sign a sublease." only expresses interest.
The fact that it took 10 days to get a copy of an agreement is suspect. Any professional real-estate agent, property manager, or landlord, knows that promptness is a requirement. "Strike while the iron is hot." is required in this business. What this tells me is that the landlord was weighing other options and settled on yours due to lack of other positive responses. Given that this appeared to be a rather short and temporary lease, it is paramount that you are settled quickly. Your landlord failed to respond in a timely manner and that often goes well in your favor in tenant landlord disputes.
I am assuming that there is no signed contract. In tenant landlord law, a lease always exists. Where there is no written lease offered by the landlord, the state default lease is in play. In order for this to happen, there must be a transaction and not just the meeting of the minds. Money and access to the property must be exchanged before any agreement and coverage under the law exists. Therefore, you have not entered into a lease agreement. No exchange has occurred.
While it might not apply in your case, I have included this here for others in the future. Where a background check and other checks are to occur, the landlord must have an application that specifically grants permission to conduct any lawful inquiries into the truthfulness of the application and any other information the landlord is entitled to such as a criminal background check, sex offender check, credit check, prior evictions check, and so on. There must be a signed grant that allows the landlord to perform this action. This application and grant does not constitute a lease agreement or contract for services. This is key. It often does not take long for an online check to occur, however, some others can take some days. I take anywhere from 4 days to 2 weeks to complete this process depending of course on what I find and how long it takes to receive information. If you filled out an application, this is not an lease agreement and is non-binding to both parties.
Can you be sued?
Not likely. However, in civil court, only the accusation needs to be made. This means that the landlord can file a complaint regardless of standing. Depending on where you are, a simple written response to the complaint should be enough. For example, I file a suit when obtaining a judgement against a bad tenant, that tenant can respond on the original complaint or in writing before the trial date. This depends upon the procedures of the state court for civil matters. It is possible with a properly written statement that the case could be dismissed prior to entering court providing that the landlord has not provided sufficient documentation with the complaint to make the case. I, as an example, always file supporting evidence with my complaint for just this reason, however, most landlords do not understand the law and often only file the complaint. So in the case where a landlord files a complaint without document evidence, the judge could read your statement, find it reasonable in the absence of supporting documentation, and dismiss the complaint before going to trial. This does happen. At the very least, the landlord could get a call from the judge or court asking for material documentation on the matter. If the landlord does not provide this information, cannot provide the requested documentation, or refuses, then a decision can be made. I have received such calls, and of course, for me it is a trivial matter of faxing the documentation or appearing in person. Assuming that the landlord has only text messages, this will not be enough.
Should you respond to this complaint?
Who knows? I would. If nothing else, you can go to the court to see what options you have within the court system given your short stay. It may be best to contact an attorney that may take this on pro-bono because of your story or at least for a very small fee. Most attorneys like to settle things over the phone quickly and this could be done in 10 minutes! You certainly have the legal right to representation even when out of the country. This is a civil case and not a criminal case so no-one is going to lock you up. However, this does effect your credit score and any background check you may have to go through for housing in the future, car loans, new credit, jobs, etc. This is enough reason for anyone to fight the case. If you are in the right, I personally would not stand for a default judgement. I am the one who sticks a finger in the air and tells them to bring it on. But that is just me. Only you can decide what to do in this matter.