Overstay of visa period

To apply for asylum you will have to do it on arrival at the airport.
If you overstay your visa you will more than likely be deported. 

Your sponsor has legal and financial responsibilities which means that they have to provide money, accommodation, assistance if you get into trouble etc and ensure you do not overstay your visa.

Yes, you will most certainly cause serious legal problems (both civil and criminal) for those who provided you with the Letter of Invitation. Such a letter carries very serious responsiblities, firstly a guarantee that you will in fact leave the country when your visa stay is over. Second to act as a guarantor for your financial sufficiency during the whole of your stay so that you would under no circumstances require any social assistance from government sources. Further if the individual providing the Letter of Invitation can be proven to have had prior knowledge of your intention to overstay they could be charged criminally with Immigration Fraud, since any false, misleading statements or omission of relevant facts in such a letter constitutes a crime.

As my friend stumpy pointed out, one may only make a claim for refugee status immediately upon arrival in a safe haven, and may not do so if they have passed first through any other safe nation upon leaving a zone of conflict. The result of trying to simply overstay now would sabotage any future attempts to obtain visas for most other countries almost as surely as a deportation order would.

My recommendation to you would be to return to your homeland, then try to travel to another country (hopefully on a new passport) since the fact that you had previously been to Belgium and received a stamp in your present passport will automatically raise the question.... "Why didn't you seek refugee status in Belgium upon arrival?" It may even raise that question using a new passport since most countries cross-reference everything from passport number, to name, country of origin and any other identifying information they have about you. They also, for the most part, share that information with other immigration authorities around the world as well.

Cheers,
William James Woodward, Expat-blog Experts Team

I can easily understand your point, but the law has to come first.
If you're from Gaza, you probably have a valid claim, but go find a lawyer and talk to him about it.
Please don't do anything illegal, and potentially cause trouble for your friends.
It would be a bad start to life in a new country.
You could also consider other countries such as Malaysia or Indonesia, where the people have Gaza have much support.
Pop to their embassies in Belgium and discuss it.

Please note - that isn't a political message - just fact.