The short answer is this. If the country of the passport you are holding recognizes common law marriage, and if you are able to convince the embassy or consulate of that country that you have a valid common law marriage, and if said embassy or consulate is willing to prepare a letter to the effect that you are common law married under the laws of your country, then probably the Singapore government will issue a LTVP (not DP) for your common law spouse.
If all of the conditions above are not met, then the chances are very high that you will not get the LTVP.
For example, the UK does not recognize common law marriage. Therefore, if you are a British Citizen, it is not possible for you to be married common law. Therefore, no British High Commission will issue you a common law marriage letter, because common law marriage does not exist. And if you cannot present a letter to the Singapore authorities that you are common law married under the laws of your country, you are not going to get the LTVP issued for your girl/boy friend.
For all of you who ask the question: You, as the EP holder, must first determine if common law marriage is a valid legal status in the country of your passport. You should verify that you can be common law married to a spouse of a different country, if your common law spouse is not from the same country as you.
If common law marriage is valid in your country/state, then the next step is to determine what the government authorities require to prove up your common law marriage, then collect that documentation. Shared home, shared bank account and credit cards, shared bills, holding yourself out as married to the public, and having each other as beneficiaries on insurance policies are examples of proof of common law marriage.
And remember, if you are successful in obtaining common law marriage, you are married just as though you got the license and had the preacher sentence you. Want to change your marital status? Get a divorce lawyer because community
property, spousal support, and child support will all apply to you.