Yes, and it takes two things. Insurable interest, which means you'd suffer a real financial loss if they died. And their consent, which means they sign the application and answer the medical questions themselves. An adult child generally has insurable interest in a parent, so the first one is rarely the obstacle. The second one is a conversation, and it's the part most people put off for years.
You can be the owner, the payer, and the beneficiary all at once, and on a policy like this you should be. Own it so it can't be changed out from under you. Pay it so it never lapses because Mom forgot. Be the beneficiary so the money lands with the person who spent it.
Which brings up a tax detail that catches people. If you own the policy and pay for it, but you name your sister as the beneficiary, the IRS can treat that death benefit as a gift from you to her. Keep the owner and the beneficiary the same person and the problem goes away. If several siblings are splitting the cost, the cleaner structure is usually each one owning a smaller policy, instead of one sibling owning a large one and promising to share.
What people buy this for: final expenses, which get into five figures fast between the funeral and the unpaid medical bills. Caregiving nobody paid them back for, which is the bigger number and almost nobody counts it. Evening out an inheritance when one child is getting the house or the business. And covering the cost of keeping a family property when the estate has no cash in it.
Cost depends almost entirely on health, and at older ages the door narrows. A healthy 68-year-old can still get fully underwritten coverage at real rates. A 78-year-old with heart disease and diabetes is usually looking at simplified issue, which means a short set of health questions and a smaller face amount. Or a guaranteed issue policy, which means no health questions at all. Understand what that last one is before you buy it. Guaranteed issue policies typically pay only your premiums back plus a little interest if death happens in the first two years, with the full benefit available after that. Skipping the health questions is what you're paying for. It's a real product with a real use, and it's a bad deal for anybody healthy enough to qualify for something else.
Expect underwriting to take longer at these ages. The carrier almost always orders an attending physician statement past 70, which means records from their regular doctor, and doctors' offices are slow. Six to ten weeks is normal. Start before the health event rather than after it. There's no version of this that works backward.
Talk to your siblings first. A policy one child owns on a parent, paid by that child, pays only that child. It's legally clean and emotionally expensive if the first anybody hears about it is at the funeral. Say what you're doing and why. If somebody wants in, they can own their own policy on the same parent. Carriers allow more than one, as long as the total lines up with a reasonable financial justification. Getting the ownership and beneficiary arrangement right the first time is a lot easier than fixing it later, which is the point of changing policy ownership. And if this policy has a job beyond the funeral, name that job now, using decide what the policy is for before you build it.