Short residential tenancies in Singapore operate largely under common law and the four corners of the tenancy agreement, because there is no general rent-control statute to fall back on. That makes the contract's own clauses on term, notice and re-entry decisive. The dealing in land itself sits under the Conveyancing and Law of Property Act 1886 (CLPA), and where the property is registered land, title moves under the Land Titles Act through the Singapore Land Authority.
The pivotal provision for any fault-based termination is section 18 of the CLPA. A right of re-entry or forfeiture for breach of a covenant is not enforceable unless the landlord first serves a notice that specifies the particular breach, requires it to be remedied if the breach is capable of remedy, and demands any compensation. The tenant must then be given a reasonable time to put things right. Skip this step and the forfeiture fails, however clear the breach. For non-payment of rent specifically, section 18A lets a tenant stop a possession action by paying the arrears and costs into court, and the court will usually grant at least four weeks before ordering possession. You can read the statute on the government's own source, the Conveyancing and Law of Property Act 1886 on Singapore Statutes Online.
Re-entry must also be peaceful and lawful. Forcing entry or changing the locks exposes a landlord to a wrongful-eviction suit, so possession is recovered through the courts where the tenant will not leave. A separate remedy exists for arrears: under the Distress Act a landlord may apply for a writ of distress to seize movable property on the premises and recover up to twelve months of unpaid rent. None of these routes is available unless the right of re-entry was expressly written into the tenancy agreement in the first place.