no US tax required as long as you are foreigner and not holding green card
No, that's incorrect in response to the original poster's question about shares in U.S. companies -- Apple, Alphabet, General Electric, Starbucks, Caterpillar, AT&T, etc., etc. (1) Non-U.S. persons owe U.S. personal income tax on the dividends (on a withholding basis when paid, at a 30% tax rate for residents of most places in the world, including non-U.S. persons residing in Singapore); and (2) U.S. estate taxes are owed on all U.S. estate taxable assets above the US$60,000 exclusion. The estate tax is due within 9 months of the stockholder's death. The estate tax return is IRS Form 706-NA.
For the record, a foreigner legally married to a U.S. person -- same or opposite sex -- can choose, with his/her spouse's agreement and cooperation, to file a joint U.S. tax return with his/her U.S. spouse. That's what's called a "Section 6013" election. Whereupon the foreigner's dividend tax rate falls to 23.8% or lower. Any excess withholding is recoverable through the joint U.S. tax filing. However, the trade-off is that the foreigner becomes subject to U.S. capital gains tax, and the foreigner's other income becomes U.S. taxable (although not necessarily taxed). Except...there's a "trick." A married foreigner can make that Section 6013 election once per lifetime and later revoke it, permanently, once per lifetime. So the "trick" is to make the election, enjoy the lower dividend tax rate, then revoke the election just before making any substantial sales of appreciated assets. Moreover, the U.S. spouse has an annual gift limit of $149,000 (2017 amount, adjusted annually for inflation) to his/her foreign spouse, so the U.S. spouse can effectively shield a substantial amount of savings from future U.S. capital gains tax. The whole reason for the $149,000 limit is to clamp down on this loophole to some degree, but US$149K/year still allows some legal game playing.
If you're trying to execute that "trick," please research it carefully. It's a little bit "sophisticated," but apparently it works for those who can manage it. I'm not necessarily recommending that "trick," although sometimes joint filing makes sense for other reasons.
Imagine, for example, that you're a foreigner married to a U.S. person, and you're working in Singapore for a startup company -- let's call it "Footbook" -- that's about to go IPO on the New York Stock Exchange. You're going to receive 5% of the shares in the company, and Footbook is expected to IPO with a total market capitalization of US$10 billion. So, overnight, you're going to receive shares worth US$500 million. Not bad! The shares are also going to pay a dividend of 2%, so that's $10 million per year. (This is a little bit of a strange startup, but bear with me -- it's just an example.) Given these sums you're going to hire a tax advisor, I'm sure. But one thing the tax advisor might recommend is that you make a Section 6013 election and file a joint return with your (much poorer!) legal American spouse, same or opposite sex. That'll save the foreigner roughly $700,000 per year in dividend taxes -- not bad again. (The U.S. income tax on the grant of the stock is unavoidable, but the joint filing very modestly reduces the tax rate on that initial grant.) Then, just prior to unloading some or most of those shares, the foreign spouse revokes the Section 6013 election. I think that works to avoid capital gains tax on appreciated Footbook shares! (Obviously that's something to triple check. I might be wrong.) Pretty great deal, right? And that hypothetical foreign spouse can still (in most cases) collect U.S. Social Security spousal benefits if his/her American spouse qualifies for his/her own retirement benefits, so that's just icing on the cake.
Marry an American, basically, if you're in that lucky position. Either gender will do.
