You may continue to use your theme, however, you have to understand that continued use of the theme will come with a chance of risk since it is no longer supported by its developers. Let me explain.
What this means is that as WordPress core developers continue to push WordPress updates (which they will do habitually in days, months, and years-to-come) with new features and security solutions through patches and new versions, the theme that you are using will not have its own developers continuing to ensure that the theme works as well with the new WordPress core updates, or as well today as it did the first day you fell in love with it. This could eventually lead to issues where as you update WordPress, you will notice the theme itself may begin to wield unruly bugs and security issues of its own that weren’t present before. This is a natural degradation of software that ultimately happens anytime that any software is no longer declared supported and as the world of other software (especially any that your software has a relationships with) continues to advance. If you understand this chance of risk and wish to continue using it anyway, then I would recommend hiring a developer to continue to support the theme, especially if your website is a highly-valued client-facing asset to your business, or a fundamental tool to the daily-workings of your internal team.
The quantitative risk is hard to assess. It really depends on how drastic any changes to WordPress core will affect the theme itself based on what parts of WordPress the theme utilizes in collaboration with any Plugins and Widgets that you use to support your website as well. You could very well go several years without a hiccup, but then wake up one morning and suddenly have a website that looks and acts in a very unsatisfying or unpredictable way.
If you decide to try and avoid this by simply turning off WordPress auto-updates or by not updating your WordPress core when regular WordPress updates are available, you may notice that your version of the WordPress core software also becomes buggy and has security flaws as hackers identify new security vulnerabilities, or as new WordPress features provided by WordPress core come to fruition and old features become legacy or outdated and also unsupported in the ways they were supported before.
Further, if you decide to freeze the updates to your copy of the WordPress core software in order to maintain your theme’s perceived integrity (visually/functionally, but still not securely because hackers), I maintain that their is still very much a risk to your website in that your hosting provider could update something as routine as its PHP version for its own security reasons or performance needs, and this could also render your website insecure, unusable, and grossly unattractive to your user-base.
This answer may seem subjective, but it isn’t. You have asked whether you can still use a theme after its developer support has ended, and will there ultimately be any risk for security/functionalities in the future. The answer is that ultimately there will be security/functionality issues in the future. It’s not necessarily a question of if, but when. So the question I would pose to you is how valuable of an asset is the website to your business, and whether you can sustain your business if this asset somehow becomes compromised.
Here’s some further reading on the issue:
https://www.wpsitecare.com/dangers-of-outdated-wordpress-plugins-themes/
https://www.quora.com/What-happens-when-a-Wordpress-theme-is-no-longer-updated
I hope that this post has armed you with enough information going forward to decide what is best for you and your business. If you have any other questions after reading through this post, feel free to add them for further guidance and support!